Matrices and linear algebra /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Schneider, Hans, 1927 Jan. 24-
Otros Autores: Barker, George Phillip
Formato: Libro
Idioma:Inglés
Publicado: New York : Dover Publications, 1989, c1973.
Edición:2nd ed.
Temas:
Álgebra lineal
Matrices.
Matrices
Acceso en línea:Publisher description
Table of contents
Tabla de Contenidos:
  • Table of Contents for Matrices and Linear Algebra: Preface to the Second Edition; Preface to the First Edition
  • I.- The Algebra of Matrices
  • 1. Matrices: Definitions
  • 2. Addition and Scalar Multiplication of Matrices
  • 3. Matrix Multiplication
  • 4. Square Matrices, Inverses, and Zero Divisors
  • 5. Transposes, Partitioning of Matrices, and Direct Sums
  • II.- Linear Equations
  • 1. Equivalent Systems of Equations
  • 2. Row Operations on Matrices
  • 3. Row Echelon Form
  • 4. Homogeneous Systems of Equations
  • 5. The Unrestricted Case: A Consistency Condition
  • 6. The Unrestricted Case: A General Solution
  • 7. Inverses of Nonsingular Matrices
  • III.- Vector Spaces
  • 1. Vectors and Vector Spaces
  • 2. Subspaces and Linear Combinations
  • 3. Linear Dependence and Linear Independence
  • 4. Bases
  • 5.tBases and Representations
  • 6. Row Spaces of Matrices
  • 7. Column Equivalence
  • 8. Row-Column Equivalence
  • 9. Equivalence Relations and Canonical Forms of Matrices
  • IV.- Determinants
  • 1. Introduction as a Volume Function
  • 2. Permutations and Permutation Matrices
  • 3. Uniqueness and Existence of the Determinant Function
  • 4. Practical Evaluation and Transposes of Determinants
  • 5. Cofactors, Minors, and Adjoints
  • 6. Determinants and Ranks
  • V.- Linear Transformations
  • 1. Definitions
  • 2. Representation of Linear Transformations
  • 3. Representations Under Change of Bases
  • VI.- Eigenvalues and Eigenvectors
  • 1. Introduction
  • 2. Relation Between Eigenvalues and Minors
  • 3. Similarity
  • 4. Algebraic and Geometric Multiplicites
  • 5.tJordan Canonical Form
  • 6. Functions of Matrices
  • 7. Application: Markov Chains
  • VII.- Inner Produce Spaces
  • 1. Inner Products
  • 2. Representation of Inner Products
  • 3. Orthogonal Bases
  • 4. Unitary Equivalence and Hermitian Matrices
  • 5. Congruence and Conjunctive Equivalence
  • 6.tCentral Conics and Quadrics
  • 7. The Natural Inverse
  • 8. Normal Matrices
  • VIII.- Applications to Differential Equations
  • 1. Introduction
  • 2. Homogeneous Differential Equations
  • 3. Linear Differrential Equations: The Unrestricted Case
  • 4. Linear Operators: The Global View
  • Answers; Symbols; Index--

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