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MARC Lista (tabellare)
Iterative Solution of Large Sparse Systems of Equations / / by Wolfgang Hackbusch
Iterative Solution of Large Sparse Systems of Equations / / by Wolfgang Hackbusch
Autore Hackbusch Wolfgang
Edizione [2nd ed. 2016.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Descrizione fisica 1 online resource (XXIII, 509 p. 26 illus., 11 illus. in color.)
Disciplina 518.26
Collana Applied Mathematical Sciences
Soggetto topico Numerical analysis
Matrix theory
Algebra
Partial differential equations
Numerical Analysis
Linear and Multilinear Algebras, Matrix Theory
Partial Differential Equations
ISBN 3-319-28483-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Part I: Linear Iterations -- Introduction -- Iterative Methods -- Classical Linear Iterations in the Positive Definite Case -- Analysis of Classical Iterations Under Special Structural Conditions -- Algebra of Linear Iterations -- Analysis of Positive Definite Iterations -- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods -- Semi-Iterative Methods -- Gradient Methods -- Conjugate Gradient Methods and Generalizations -- Part III: Special Iterations -- Multigrid Iterations -- Domain Decomposition and Subspace Methods -- H-LU Iteration -- Tensor-based Methods -- Appendices.
Record Nr. UNINA-9910254096203321
Hackbusch Wolfgang  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Materiale a stampa
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Large Random Matrices: Lectures on Macroscopic Asymptotics [[electronic resource] ] : École d'Été de Probabilités de Saint-Flour XXXVI – 2006 / / by Alice Guionnet
Large Random Matrices: Lectures on Macroscopic Asymptotics [[electronic resource] ] : École d'Été de Probabilités de Saint-Flour XXXVI – 2006 / / by Alice Guionnet
Autore Guionnet Alice
Edizione [1st ed. 2009.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2009
Descrizione fisica 1 online resource (XII, 294 p. 13 illus.)
Disciplina 512.9434
Collana École d'Été de Probabilités de Saint-Flour
Soggetto topico Discrete mathematics
Probabilities
Algebra
Matrix theory
Functional analysis
Combinatorics
Discrete Mathematics
Probability Theory and Stochastic Processes
Linear and Multilinear Algebras, Matrix Theory
Functional Analysis
ISBN 3-540-69897-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Wigner matrices and moments estimates -- Wigner#x2019;s theorem -- Wigner's matrices; more moments estimates -- Words in several independent Wigner matrices -- Wigner matrices and concentration inequalities -- Concentration inequalities and logarithmic Sobolev inequalities -- Generalizations -- Concentration inequalities for random matrices -- Matrix models -- Maps and Gaussian calculus -- First-order expansion -- Second-order expansion for the free energy -- Eigenvalues of Gaussian Wigner matrices and large deviations -- Large deviations for the law of the spectral measure of Gaussian Wigner's matrices -- Large Deviations of the Maximum Eigenvalue -- Stochastic calculus -- Stochastic analysis for random matrices -- Large deviation principle for the law of the spectral measure of shifted Wigner matrices -- Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials -- Asymptotics of some matrix integrals -- Free probability -- Free probability setting -- Freeness -- Free entropy -- Basics of matrices -- Basics of probability theory.
Record Nr. UNISA-996466482503316
Guionnet Alice  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2009
Materiale a stampa
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Large truncated Toeplitz matrices, Toeplitz operators, and related topics : the Albrecht Böttcher anniversary volume / / edited by Dario A. Bini, Torsten Ehrhardt, Alexei Yu. Karlovich, Ilya Spitkovsky
Large truncated Toeplitz matrices, Toeplitz operators, and related topics : the Albrecht Böttcher anniversary volume / / edited by Dario A. Bini, Torsten Ehrhardt, Alexei Yu. Karlovich, Ilya Spitkovsky
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Descrizione fisica 1 online resource (XXVI, 740 p. 61 illus., 30 illus. in color.)
Disciplina 512.5
Collana Operator Theory: Advances and Applications
Soggetto topico Matrix theory
Algebra
Operator theory
Linear and Multilinear Algebras, Matrix Theory
Operator Theory
ISBN 3-319-49182-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Publications of Albrecht Böttcher.- Albrecht Böttcher - 20 Years of Friendship and Joint Work.- Salutatory with regards from the mathematics students of Chemnitz.- Essay on Albrecht Böttcher.- Meeting Albrecht the Strong.- The beginning (the way I remember it) -- Personal Address on the Occasion of Albrecht Böttcher's 60th Birthday -- Asymptotics of eigenvalues for pentadiagonal symmetric Toeplitz matrices -- Echelon type canonical forms in upper triangular matrix algebras -- Asymptotic formulas for determinants of a special class of Toeplitz + Hankel matrices -- Generalization of the Brauer Theorem to Matrix Polynomials and Matrix Laurent Series -- Eigenvalues of Hermitian Toeplitz matrices generated by simple-loop symbols with relaxed smoothness -- On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II -- Useful bounds on the extreme eigenvalues and vectors of matrices for Harper's operators -- Fast inversion of centrosymmetric Toeplitz-plus-Hankel Bezoutians -- On Matrix-Valued Stieltjes Functions with an Emphasis on Particular Subclasses -- The theory of Generalized Locally Toeplitz sequences: a review, an extension, and a few representative applications -- The Bézout equation on the right half plane in a Wiener space setting -- On a collocation-quadrature method for the singular integral equation of the notched half plane problem -- The Haseman Boundary Value Problem with Slowly Oscillating Coefficients and Shifts -- On the Norm of Linear Combinations of Projections and Some Characterizations of Hilbert Spaces -- Pseudodifferential Operators in Weighted Hölder-Zygmund Spaces of Variable Smoothness -- Commutator estimates comprising the Frobenius norm - Looking back and forth.- Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions on the Boundary -- Traces on operator ideals and related linear forms on sequence ideals (part IV).- Error estimates for the ESPRIT algorithm -- The universal algebra generated by a power partial isometry -- Norms, condition numbers and pseudospectra of convolution type operators on intervals.- Paired operators in asymmetric space setting -- Natural Boundary for a Sum Involving Toeplitz Determinants.- A Riemann-Hilbert Approach to Filter Design.
Record Nr. UNINA-9910254307803321
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Lernbuch Lineare Algebra und Analytische Geometrie : Das Wichtigste ausführlich für das Lehramts- und Bachelorstudium / / von Gerd Fischer
Lernbuch Lineare Algebra und Analytische Geometrie : Das Wichtigste ausführlich für das Lehramts- und Bachelorstudium / / von Gerd Fischer
Autore Fischer Gerd
Edizione [3rd ed. 2017.]
Pubbl/distr/stampa Wiesbaden : , : Springer Fachmedien Wiesbaden : , : Imprint : Springer Spektrum, , 2017
Descrizione fisica 1 online resource (XI, 479 S. 133 Abb., 87 Abb. in Farbe.)
Disciplina 512.5
Soggetto topico Matrix theory
Algebra
Linear and Multilinear Algebras, Matrix Theory
ISBN 3-658-18191-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione ger
Nota di contenuto Lineare Geometrie im n-dimensionalen reellen Raum -- Grundlagen (Mengen, Gruppen, Körper, Polynome) -- Vektorräume, lineare Abbildungen und Matrizen -- Determinanten -- Eigenwerte und Normalformen -- Bilineare Algebra und Geometrie.
Record Nr. UNINA-9910483328303321
Fischer Gerd  
Wiesbaden : , : Springer Fachmedien Wiesbaden : , : Imprint : Springer Spektrum, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Linear Algebra [[electronic resource] /] / by Jörg Liesen, Volker Mehrmann
Linear Algebra [[electronic resource] /] / by Jörg Liesen, Volker Mehrmann
Autore Liesen Jörg
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (XI, 324 p. 22 illus.)
Disciplina 512.5
Collana Springer Undergraduate Mathematics Series
Soggetto topico Matrix theory
Algebra
Linear and Multilinear Algebras, Matrix Theory
ISBN 3-319-24346-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Linear Algebra in every day life -- Basic mathematical concepts -- Algebraic structures -- Matrices -- The echelon form and the rank of matrices -- Linear systems of equations -- Determinants of matrices -- The characteristic polynomial and eigenvalues of matrices -- Vector spaces -- Linear maps -- Linear forms and bilinear forms -- Euclidean and unitary vector spaces -- Adjoints of linear maps -- Eigenvalues of endomorphisms -- Polynomials and the Fundamental Theorem of Algebra -- Cyclic subspaces, duality and the Jordan canonical form -- Matrix functions and systems of differential equations -- Special classes of endomorphisms -- The singular value decomposition -- The Kronecker product and linear matrix equations.
Record Nr. UNINA-9910300259803321
Liesen Jörg  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
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Linear Algebra / / by M. Thamban Nair, Arindama Singh
Linear Algebra / / by M. Thamban Nair, Arindama Singh
Autore Nair M. Thamban
Edizione [1st ed. 2018.]
Pubbl/distr/stampa Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018
Descrizione fisica 1 online resource (XI, 341 p. 2 illus.)
Disciplina 551.48
Soggetto topico Algebras, Linear
Matrix theory
Algebra
Mathematics—Study and teaching 
Linear Algebra
Linear and Multilinear Algebras, Matrix Theory
Mathematics Education
ISBN 981-13-0926-4
978-981-13-0926-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. Vector Spaces -- Chapter 2. Linear Transformations -- Chapter 3. Elementary Operations -- Chapter 4. Inner Product Spaces -- Chapter 5. Eigenvalues and Eigenvectors -- Chapter 6. Block Diagonal Representation -- Chapter 7. Spectral Decomposition.
Record Nr. UNINA-9910300119703321
Nair M. Thamban  
Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Linear Algebra / / by Belkacem Said-Houari
Linear Algebra / / by Belkacem Said-Houari
Autore Said-Houari Belkacem
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Descrizione fisica 1 online resource (XIII, 384 p. 26 illus. in color.)
Disciplina 512.5
Collana Compact Textbooks in Mathematics
Soggetto topico Matrix theory
Algebra
Linear and Multilinear Algebras, Matrix Theory
ISBN 3-319-63793-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Matrices and matrix operations -- Determinants -- General vector spaces -- Linear transformations -- Linear transformations and matrices -- Eigenvalues and eigenvectors -- Orthogonal matrices and quadratic forms.
Record Nr. UNINA-9910254284903321
Said-Houari Belkacem  
Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Linear Algebra [[electronic resource] /] / by Larry Smith
Linear Algebra [[electronic resource] /] / by Larry Smith
Autore Smith Larry
Edizione [3rd ed. 1998.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1998
Descrizione fisica 1 online resource (XII, 454 p.)
Disciplina 512.5
Collana Undergraduate Texts in Mathematics
Soggetto topico Matrix theory
Algebra
Linear and Multilinear Algebras, Matrix Theory
ISBN 1-4612-1670-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Vectors in the Plane and in Space -- 1.1 First Steps -- 1.2 Exercises -- 2. Vector Spaces -- 2.1 Axioms for Vector Spaces -- 2.2 Cartesian (or Euclidean) Spaces -- 2.3 Some Rules for Vector Algebra -- 2.4 Exercises -- 3. Examples of Vector Spaces -- 3.1 Three Basic Examples -- 3.2 Further Examples of Vector Spaces -- 3.3 Exercises -- 4. Subspaces -- 4.1 Basic Properties of Vector Subspaces -- 4.2 Examples of Subspaces -- 4.3 Exercises -- 5. Linear Independence and Dependence -- 5.1 Basic Definitions and Examples -- 5.2 Properties of Independent and Dependent Sets -- 5.3 Exercises -- 6. Finite-Dimensional Vector Spaces and Bases -- 6.1 Finite-Dimensional Vector Spaces -- 6.2 Properties of Bases -- 6.3 Using Bases -- 6.4 Exercises -- 7. The Elements of Vector Spaces: A Summing Up -- 7.1 Numerical Examples -- 7.2 Exercises -- 8. Linear Transformations -- 8.1 Definition of Linear Transformations -- 8.2 Examples of Linear Transformations -- 8.3 Properties of Linear Transformations -- 8.4 Images and Kernels of Linear Transformations -- 8.5 Some Fundamental Constructions -- 8.6 Isomorphism of Vector Spaces -- 8.7 Exercises -- 9. Linear Transformations: Examples and Applications -- 9.1 Numerical Examples -- 9.2 Some Applications -- 9.3 Exercises -- 10. Linear Transformations and Matrices -- 10.1 Linear Transformations and Matrices in IR3 -- 10.2 Some Numerical Examples -- 10.3 Matrices and Their Algebra -- 10.4 Special Types of Matrices -- 10.5 Exercises -- 11. Representing Linear Transformations by Matrices -- 11.1 Representing a Linear Transformation by a Matrix -- 11.2 Basic Theorems -- 11.3 Change of Bases -- 11.4 Exercises -- 12. More on Representing Linear Transformations by Matrices -- 12.1 Projections -- 12.2 Nilpotent Transformations -- 12.3 Cyclic Transformations -- 12.4 Exercises -- 13. Systems of Linear Equations -- 13.1 Existence Theorems -- 13.2 Reduction to Echelon Form -- 13.3 The Simplex Method -- 13.4 Exercises -- 14. The Elements of Eigenvalue and Eigenvector Theory -- 14.1 The Rank of an Endomorphism -- 14.2 Eigenvalues and Eigenvectors -- 14.3 Determinants -- 14.4 The Characteristic Polynomial -- 14.5 Diagonalization Theorems -- 14.6 Exercises -- 15. Inner Product Spaces -- 15.1 Scalar Products -- 15.2 Inner Product Spaces -- 15.3 Isometries -- 15.4 The Riesz Representation Theorem -- 15.5 Legendre Polynomials -- 15.6 Exercises -- 16. The Spectral Theorem and Quadratic Forms -- 16.1 Self-Adjoint Transformations -- 16.2 The Spectral Theorem -- 16.3 The Principal Axis Theorem for Quadratic Forms -- 16.4 A Proof of the Spectral Theorem in the General Case -- 16.5 Exercises -- 17. Jordan Canonical Form -- 17.1 Invariant Subspaces -- 17.2 Nilpotent Transformations -- 17.3 The Jordan Normal Form -- 17.4 Square Roots -- 17.5 The Hamilton-Cayley Theorem -- 17.6 Inverses -- 17.7 Exercises -- 18. Application to Differential Equations -- 18.1 Linear Differential Systems: Basic Definitions -- 18.2 Diagonalizable Systems -- 18.3 Application of Jordan Form -- 18.4 Exercises -- 19. The Similarity Problem -- 19.1 The Fundamental Problem of Linear Algebra -- 19.2 A Bit of Invariant Theory -- 19.3 Exercises -- A. Multilinear Algebra and Determinants -- A.1 Multilinear Forms -- A.2 Determinants -- A.3 Exercises -- B. Complex Numbers -- B.1 The Complex Numbers -- B.2 Exercises -- Font Usage -- Notations.
Record Nr. UNINA-9910480418803321
Smith Larry  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1998
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Linear Algebra [[electronic resource] /] / by Larry Smith
Linear Algebra [[electronic resource] /] / by Larry Smith
Autore Smith Larry
Edizione [3rd ed. 1998.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1998
Descrizione fisica 1 online resource (XII, 454 p.)
Disciplina 512.5
Collana Undergraduate Texts in Mathematics
Soggetto topico Matrix theory
Algebra
Linear and Multilinear Algebras, Matrix Theory
ISBN 1-4612-1670-2
Classificazione 15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Vectors in the Plane and in Space -- 1.1 First Steps -- 1.2 Exercises -- 2. Vector Spaces -- 2.1 Axioms for Vector Spaces -- 2.2 Cartesian (or Euclidean) Spaces -- 2.3 Some Rules for Vector Algebra -- 2.4 Exercises -- 3. Examples of Vector Spaces -- 3.1 Three Basic Examples -- 3.2 Further Examples of Vector Spaces -- 3.3 Exercises -- 4. Subspaces -- 4.1 Basic Properties of Vector Subspaces -- 4.2 Examples of Subspaces -- 4.3 Exercises -- 5. Linear Independence and Dependence -- 5.1 Basic Definitions and Examples -- 5.2 Properties of Independent and Dependent Sets -- 5.3 Exercises -- 6. Finite-Dimensional Vector Spaces and Bases -- 6.1 Finite-Dimensional Vector Spaces -- 6.2 Properties of Bases -- 6.3 Using Bases -- 6.4 Exercises -- 7. The Elements of Vector Spaces: A Summing Up -- 7.1 Numerical Examples -- 7.2 Exercises -- 8. Linear Transformations -- 8.1 Definition of Linear Transformations -- 8.2 Examples of Linear Transformations -- 8.3 Properties of Linear Transformations -- 8.4 Images and Kernels of Linear Transformations -- 8.5 Some Fundamental Constructions -- 8.6 Isomorphism of Vector Spaces -- 8.7 Exercises -- 9. Linear Transformations: Examples and Applications -- 9.1 Numerical Examples -- 9.2 Some Applications -- 9.3 Exercises -- 10. Linear Transformations and Matrices -- 10.1 Linear Transformations and Matrices in IR3 -- 10.2 Some Numerical Examples -- 10.3 Matrices and Their Algebra -- 10.4 Special Types of Matrices -- 10.5 Exercises -- 11. Representing Linear Transformations by Matrices -- 11.1 Representing a Linear Transformation by a Matrix -- 11.2 Basic Theorems -- 11.3 Change of Bases -- 11.4 Exercises -- 12. More on Representing Linear Transformations by Matrices -- 12.1 Projections -- 12.2 Nilpotent Transformations -- 12.3 Cyclic Transformations -- 12.4 Exercises -- 13. Systems of Linear Equations -- 13.1 Existence Theorems -- 13.2 Reduction to Echelon Form -- 13.3 The Simplex Method -- 13.4 Exercises -- 14. The Elements of Eigenvalue and Eigenvector Theory -- 14.1 The Rank of an Endomorphism -- 14.2 Eigenvalues and Eigenvectors -- 14.3 Determinants -- 14.4 The Characteristic Polynomial -- 14.5 Diagonalization Theorems -- 14.6 Exercises -- 15. Inner Product Spaces -- 15.1 Scalar Products -- 15.2 Inner Product Spaces -- 15.3 Isometries -- 15.4 The Riesz Representation Theorem -- 15.5 Legendre Polynomials -- 15.6 Exercises -- 16. The Spectral Theorem and Quadratic Forms -- 16.1 Self-Adjoint Transformations -- 16.2 The Spectral Theorem -- 16.3 The Principal Axis Theorem for Quadratic Forms -- 16.4 A Proof of the Spectral Theorem in the General Case -- 16.5 Exercises -- 17. Jordan Canonical Form -- 17.1 Invariant Subspaces -- 17.2 Nilpotent Transformations -- 17.3 The Jordan Normal Form -- 17.4 Square Roots -- 17.5 The Hamilton-Cayley Theorem -- 17.6 Inverses -- 17.7 Exercises -- 18. Application to Differential Equations -- 18.1 Linear Differential Systems: Basic Definitions -- 18.2 Diagonalizable Systems -- 18.3 Application of Jordan Form -- 18.4 Exercises -- 19. The Similarity Problem -- 19.1 The Fundamental Problem of Linear Algebra -- 19.2 A Bit of Invariant Theory -- 19.3 Exercises -- A. Multilinear Algebra and Determinants -- A.1 Multilinear Forms -- A.2 Determinants -- A.3 Exercises -- B. Complex Numbers -- B.1 The Complex Numbers -- B.2 Exercises -- Font Usage -- Notations.
Record Nr. UNINA-9910789226603321
Smith Larry  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1998
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebra / / by Larry Smith
Linear Algebra / / by Larry Smith
Autore Smith Larry
Edizione [3rd ed. 1998.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1998
Descrizione fisica 1 online resource (XII, 454 p.)
Disciplina 512.5
Collana Undergraduate Texts in Mathematics
Soggetto topico Matrix theory
Algebra
Linear and Multilinear Algebras, Matrix Theory
ISBN 1-4612-1670-2
Classificazione 15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Vectors in the Plane and in Space -- 1.1 First Steps -- 1.2 Exercises -- 2. Vector Spaces -- 2.1 Axioms for Vector Spaces -- 2.2 Cartesian (or Euclidean) Spaces -- 2.3 Some Rules for Vector Algebra -- 2.4 Exercises -- 3. Examples of Vector Spaces -- 3.1 Three Basic Examples -- 3.2 Further Examples of Vector Spaces -- 3.3 Exercises -- 4. Subspaces -- 4.1 Basic Properties of Vector Subspaces -- 4.2 Examples of Subspaces -- 4.3 Exercises -- 5. Linear Independence and Dependence -- 5.1 Basic Definitions and Examples -- 5.2 Properties of Independent and Dependent Sets -- 5.3 Exercises -- 6. Finite-Dimensional Vector Spaces and Bases -- 6.1 Finite-Dimensional Vector Spaces -- 6.2 Properties of Bases -- 6.3 Using Bases -- 6.4 Exercises -- 7. The Elements of Vector Spaces: A Summing Up -- 7.1 Numerical Examples -- 7.2 Exercises -- 8. Linear Transformations -- 8.1 Definition of Linear Transformations -- 8.2 Examples of Linear Transformations -- 8.3 Properties of Linear Transformations -- 8.4 Images and Kernels of Linear Transformations -- 8.5 Some Fundamental Constructions -- 8.6 Isomorphism of Vector Spaces -- 8.7 Exercises -- 9. Linear Transformations: Examples and Applications -- 9.1 Numerical Examples -- 9.2 Some Applications -- 9.3 Exercises -- 10. Linear Transformations and Matrices -- 10.1 Linear Transformations and Matrices in IR3 -- 10.2 Some Numerical Examples -- 10.3 Matrices and Their Algebra -- 10.4 Special Types of Matrices -- 10.5 Exercises -- 11. Representing Linear Transformations by Matrices -- 11.1 Representing a Linear Transformation by a Matrix -- 11.2 Basic Theorems -- 11.3 Change of Bases -- 11.4 Exercises -- 12. More on Representing Linear Transformations by Matrices -- 12.1 Projections -- 12.2 Nilpotent Transformations -- 12.3 Cyclic Transformations -- 12.4 Exercises -- 13. Systems of Linear Equations -- 13.1 Existence Theorems -- 13.2 Reduction to Echelon Form -- 13.3 The Simplex Method -- 13.4 Exercises -- 14. The Elements of Eigenvalue and Eigenvector Theory -- 14.1 The Rank of an Endomorphism -- 14.2 Eigenvalues and Eigenvectors -- 14.3 Determinants -- 14.4 The Characteristic Polynomial -- 14.5 Diagonalization Theorems -- 14.6 Exercises -- 15. Inner Product Spaces -- 15.1 Scalar Products -- 15.2 Inner Product Spaces -- 15.3 Isometries -- 15.4 The Riesz Representation Theorem -- 15.5 Legendre Polynomials -- 15.6 Exercises -- 16. The Spectral Theorem and Quadratic Forms -- 16.1 Self-Adjoint Transformations -- 16.2 The Spectral Theorem -- 16.3 The Principal Axis Theorem for Quadratic Forms -- 16.4 A Proof of the Spectral Theorem in the General Case -- 16.5 Exercises -- 17. Jordan Canonical Form -- 17.1 Invariant Subspaces -- 17.2 Nilpotent Transformations -- 17.3 The Jordan Normal Form -- 17.4 Square Roots -- 17.5 The Hamilton-Cayley Theorem -- 17.6 Inverses -- 17.7 Exercises -- 18. Application to Differential Equations -- 18.1 Linear Differential Systems: Basic Definitions -- 18.2 Diagonalizable Systems -- 18.3 Application of Jordan Form -- 18.4 Exercises -- 19. The Similarity Problem -- 19.1 The Fundamental Problem of Linear Algebra -- 19.2 A Bit of Invariant Theory -- 19.3 Exercises -- A. Multilinear Algebra and Determinants -- A.1 Multilinear Forms -- A.2 Determinants -- A.3 Exercises -- B. Complex Numbers -- B.1 The Complex Numbers -- B.2 Exercises -- Font Usage -- Notations.
Record Nr. UNINA-9910818805503321
Smith Larry  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1998
Materiale a stampa
Lo trovi qui: Univ. Federico II
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