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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
Opac: Controlla la disponibilità qui
Linear Algebra [[electronic resource] ] : An Introduction to Abstract Mathematics / / by Robert J. Valenza
Linear Algebra [[electronic resource] ] : An Introduction to Abstract Mathematics / / by Robert J. Valenza
Autore Valenza Robert J
Edizione [1st ed. 1993.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1993
Descrizione fisica 1 online resource (XVIII, 237 p.)
Disciplina 512
Collana Undergraduate Texts in Mathematics
Soggetto topico Algebra
Matrix theory
Linear and Multilinear Algebras, Matrix Theory
ISBN 1-4612-0901-3
Classificazione 15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Sets and Functions -- 1.1 Notation and Terminology -- 1.2 Composition of Functions -- 1.3 Inverse Functions -- 1.4 Digression on Cardinality -- 1.5 Permutations -- Exercises -- 2 Groups and Group Homomorphisms -- 2.1 Groups and Subgroups -- 2.2 Group Homomorphisms -- 2.3 Rings and Fields -- Exercises -- 3 Vector Spaces and Linear Transformations -- 3.1 Vector Spaces and Subspaces -- 3.2 Linear Transformations -- 3.3 Direct Products and Internal Direct Sums -- Exercises -- 4 Dimension -- 4.1 Bases and Dimension -- 4.2 Vector Spaces Are Free -- 4.3 Rank and Nullity -- Exercises -- 5 Matrices -- 5.1 Notation and Terminology -- 5.2 Introduction to Linear Systems -- 5.3 Solution Techniques -- 5.4 Multiple Systems and Matrix Inversion -- Exercises -- 6 Representation of Linear Transformations -- 6.1 The Space of Linear Transformations -- 6.2 The Representation of Hom(kn,km) -- 6.3 The Representation of Hom(V,V’) -- 6.4 The Dual Space -- 6.5 Change of Basis -- Exercises -- 7 Inner Product Spaces -- 7.1 Real Inner Product Spaces -- 7.2 Orthogonal Bases and Orthogonal Projection -- 7.3 Complex Inner Product Spaces -- Exercises -- 8 Determinants -- 8.1 Existence and Basic Properties -- 8.2 A Nonrecursive Formula; Uniqueness -- 8.3 The Determinant of a Product; Invertibility -- Exercises -- 9 Eigenvalues and Eigenvectors -- 9.1 Definitions and Elementary Properties -- 9.2 Hermitian and Unitary Transformations -- 9.3 Spectral Decomposition -- Exercises -- 10 Triangulation and Decomposition of Endomorphisms -- 10.1 The Cayley-Hamilton Theorem -- 10.2 Triangulation of Endomorphisms -- 10.3 Decomposition by Characteristic Subspaces -- 10.4 Nilpotent Mappings and the Jordan Normal Form -- Exercises -- Supplementary Topics -- 1 Differentiation -- 2 The Determinant Revisited -- 3 Quadratic Forms -- 4 An Introduction to Categories and Functors.
Record Nr. UNINA-9910480324103321
Valenza Robert J  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1993
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebra [[electronic resource] ] : An Introduction to Abstract Mathematics / / by Robert J. Valenza
Linear Algebra [[electronic resource] ] : An Introduction to Abstract Mathematics / / by Robert J. Valenza
Autore Valenza Robert J
Edizione [1st ed. 1993.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1993
Descrizione fisica 1 online resource (XVIII, 237 p.)
Disciplina 512
Collana Undergraduate Texts in Mathematics
Soggetto topico Algebra
Matrix theory
Linear and Multilinear Algebras, Matrix Theory
ISBN 1-4612-0901-3
Classificazione 15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Sets and Functions -- 1.1 Notation and Terminology -- 1.2 Composition of Functions -- 1.3 Inverse Functions -- 1.4 Digression on Cardinality -- 1.5 Permutations -- Exercises -- 2 Groups and Group Homomorphisms -- 2.1 Groups and Subgroups -- 2.2 Group Homomorphisms -- 2.3 Rings and Fields -- Exercises -- 3 Vector Spaces and Linear Transformations -- 3.1 Vector Spaces and Subspaces -- 3.2 Linear Transformations -- 3.3 Direct Products and Internal Direct Sums -- Exercises -- 4 Dimension -- 4.1 Bases and Dimension -- 4.2 Vector Spaces Are Free -- 4.3 Rank and Nullity -- Exercises -- 5 Matrices -- 5.1 Notation and Terminology -- 5.2 Introduction to Linear Systems -- 5.3 Solution Techniques -- 5.4 Multiple Systems and Matrix Inversion -- Exercises -- 6 Representation of Linear Transformations -- 6.1 The Space of Linear Transformations -- 6.2 The Representation of Hom(kn,km) -- 6.3 The Representation of Hom(V,V’) -- 6.4 The Dual Space -- 6.5 Change of Basis -- Exercises -- 7 Inner Product Spaces -- 7.1 Real Inner Product Spaces -- 7.2 Orthogonal Bases and Orthogonal Projection -- 7.3 Complex Inner Product Spaces -- Exercises -- 8 Determinants -- 8.1 Existence and Basic Properties -- 8.2 A Nonrecursive Formula; Uniqueness -- 8.3 The Determinant of a Product; Invertibility -- Exercises -- 9 Eigenvalues and Eigenvectors -- 9.1 Definitions and Elementary Properties -- 9.2 Hermitian and Unitary Transformations -- 9.3 Spectral Decomposition -- Exercises -- 10 Triangulation and Decomposition of Endomorphisms -- 10.1 The Cayley-Hamilton Theorem -- 10.2 Triangulation of Endomorphisms -- 10.3 Decomposition by Characteristic Subspaces -- 10.4 Nilpotent Mappings and the Jordan Normal Form -- Exercises -- Supplementary Topics -- 1 Differentiation -- 2 The Determinant Revisited -- 3 Quadratic Forms -- 4 An Introduction to Categories and Functors.
Record Nr. UNINA-9910789344503321
Valenza Robert J  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1993
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear Algebra : An Introduction to Abstract Mathematics / / by Robert J. Valenza
Linear Algebra : An Introduction to Abstract Mathematics / / by Robert J. Valenza
Autore Valenza Robert J
Edizione [1st ed. 1993.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1993
Descrizione fisica 1 online resource (XVIII, 237 p.)
Disciplina 512
Collana Undergraduate Texts in Mathematics
Soggetto topico Algebra
Matrix theory
Linear and Multilinear Algebras, Matrix Theory
ISBN 1-4612-0901-3
Classificazione 15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Sets and Functions -- 1.1 Notation and Terminology -- 1.2 Composition of Functions -- 1.3 Inverse Functions -- 1.4 Digression on Cardinality -- 1.5 Permutations -- Exercises -- 2 Groups and Group Homomorphisms -- 2.1 Groups and Subgroups -- 2.2 Group Homomorphisms -- 2.3 Rings and Fields -- Exercises -- 3 Vector Spaces and Linear Transformations -- 3.1 Vector Spaces and Subspaces -- 3.2 Linear Transformations -- 3.3 Direct Products and Internal Direct Sums -- Exercises -- 4 Dimension -- 4.1 Bases and Dimension -- 4.2 Vector Spaces Are Free -- 4.3 Rank and Nullity -- Exercises -- 5 Matrices -- 5.1 Notation and Terminology -- 5.2 Introduction to Linear Systems -- 5.3 Solution Techniques -- 5.4 Multiple Systems and Matrix Inversion -- Exercises -- 6 Representation of Linear Transformations -- 6.1 The Space of Linear Transformations -- 6.2 The Representation of Hom(kn,km) -- 6.3 The Representation of Hom(V,V’) -- 6.4 The Dual Space -- 6.5 Change of Basis -- Exercises -- 7 Inner Product Spaces -- 7.1 Real Inner Product Spaces -- 7.2 Orthogonal Bases and Orthogonal Projection -- 7.3 Complex Inner Product Spaces -- Exercises -- 8 Determinants -- 8.1 Existence and Basic Properties -- 8.2 A Nonrecursive Formula; Uniqueness -- 8.3 The Determinant of a Product; Invertibility -- Exercises -- 9 Eigenvalues and Eigenvectors -- 9.1 Definitions and Elementary Properties -- 9.2 Hermitian and Unitary Transformations -- 9.3 Spectral Decomposition -- Exercises -- 10 Triangulation and Decomposition of Endomorphisms -- 10.1 The Cayley-Hamilton Theorem -- 10.2 Triangulation of Endomorphisms -- 10.3 Decomposition by Characteristic Subspaces -- 10.4 Nilpotent Mappings and the Jordan Normal Form -- Exercises -- Supplementary Topics -- 1 Differentiation -- 2 The Determinant Revisited -- 3 Quadratic Forms -- 4 An Introduction to Categories and Functors.
Record Nr. UNINA-9910812419203321
Valenza Robert J  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1993
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Undergraduate Algebra [[electronic resource] /] / by Serge Lang
Undergraduate Algebra [[electronic resource] /] / by Serge Lang
Autore Lang Serge
Edizione [2nd ed. 1990.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (XI, 371 p.)
Disciplina 512
Collana Undergraduate Texts in Mathematics
Soggetto topico Algebra
ISBN 1-4757-6898-2
Classificazione 13-01
15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto I The Integers -- II Groups -- III Rings -- IV Polynomials -- V Vector Spaces and Modules -- VI Some Linear Groups -- VII Field Theory -- VIII Finite Fields -- IX The Real and Complex Numbers -- X Sets -- §1. The Natural Numbers -- §2. The Integers -- §3. Infinite Sets.
Record Nr. UNINA-9910480199603321
Lang Serge  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Undergraduate Algebra [[electronic resource] /] / by Serge Lang
Undergraduate Algebra [[electronic resource] /] / by Serge Lang
Autore Lang Serge
Edizione [2nd ed. 1990.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (XI, 371 p.)
Disciplina 512
Collana Undergraduate Texts in Mathematics
Soggetto topico Algebra
ISBN 1-4757-6898-2
Classificazione 13-01
15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto I The Integers -- II Groups -- III Rings -- IV Polynomials -- V Vector Spaces and Modules -- VI Some Linear Groups -- VII Field Theory -- VIII Finite Fields -- IX The Real and Complex Numbers -- X Sets -- §1. The Natural Numbers -- §2. The Integers -- §3. Infinite Sets.
Record Nr. UNINA-9910792489003321
Lang Serge  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Undergraduate Algebra / / by Serge Lang
Undergraduate Algebra / / by Serge Lang
Autore Lang Serge
Edizione [2nd ed. 1990.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (XI, 371 p.)
Disciplina 512
Collana Undergraduate Texts in Mathematics
Soggetto topico Algebra
ISBN 1-4757-6898-2
Classificazione 13-01
15-01
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto I The Integers -- II Groups -- III Rings -- IV Polynomials -- V Vector Spaces and Modules -- VI Some Linear Groups -- VII Field Theory -- VIII Finite Fields -- IX The Real and Complex Numbers -- X Sets -- §1. The Natural Numbers -- §2. The Integers -- §3. Infinite Sets.
Record Nr. UNINA-9910821727603321
Lang Serge  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui