Matrices and Linear Algebra

ISBN-10: 0486660141

ISBN-13: 9780486660141

Edition: 2nd 1989

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Book details

List price: $17.95
Edition: 2nd
Copyright year: 1989
Publisher: Dover Publications, Incorporated
Publication date: 6/1/1989
Binding: Paperback
Pages: 432
Size: 5.50" wide x 8.50" long x 1.00" tall
Weight: 0.946
Language: English

Preface to the Second Edition
Preface to the First Edition
The Algebra of Matrices
Matrices: Definitions
Addition and Scalar Multiplication of Matrices
Matrix Multiplication
Square Matrices, Inverses, and Zero Divisors
Transposes, Partitioning of Matrices, and Direct Sums
Linear Equations
Equivalent Systems of Equations
Row Operations on Matrices
Row Echelon Form
Homogeneous Systems of Equations
The Unrestricted Case: A Consistency Condition
The Unrestricted Case: A General Solution
Inverses of Nonsingular Matrices
Vector Spaces
Vectors and Vector Spaces
Subspaces and Linear Combinations
Linear Dependence and Linear Independence
Bases and Representations
Row Spaces of Matrices
Column Equivalence
Row-Column Equivalence
Equivalence Relations and Canonical Forms of Matrices
Introduction as a Volume Function
Permutations and Permutation Matrices
Uniqueness and Existence of the Determinant Function
Practical Evaluation and Transposes of Determinants
Cofactors, Minors, and Adjoints
Determinants and Ranks
Linear Transformations
Representation of Linear Transformations
Representations Under Change of Bases
Eigenvalues and Eigenvectors
Relation Between Eigenvalues and Minors
Algebraic and Geometric Multiplicites
Jordan Canonical Form
Functions of Matrices
Application: Markov Chains
Inner Produce Spaces
Inner Products
Representation of Inner Products
Orthogonal Bases
Unitary Equivalence and Hermitian Matrices
Congruence and Conjunctive Equivalence
Central Conics and Quadrics
The Natural Inverse
Normal Matrices
Applications to Differential Equations
Homogeneous Differential Equations
Linear Differrential Equations: The Unrestricted Case
Linear Operators: The Global Vie?
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