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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 | ||
| ||
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 | ||
| ||
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 | ||
| ||