Matrices and Linear Algebra / Edition 2

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New York, etc Hard cover 2nd Revised edition. Revised. Fair. No dust jacket. Water stained copy but just edges of some of the back pages. Very little writing in the book Inside ... text is fine Item ships media mail only 420 p. Read more Show Less

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Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues and differential equations. Numerous exercises, both true-false and multiple choice, with each chapter. Answer section.
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Product Details

  • ISBN-13: 9780030914027
  • Publisher: Holt McDougal
  • Publication date: 1/1/1973
  • Edition number: 2
  • Pages: 413

Table of Contents

  Preface to the Second Edition; Preface to the First Edition
1. 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
2. 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
3. Vector Spaces
  1. Vectors and Vector Spaces
  2. Subspaces and Linear Combinations
  3. Linear Dependence and Linear Independence
  4. Bases
  5. Bases and Representations
  6. Row Spaces of Matrices
  7. Column Equivalence
  8. Row-Column Equivalence
  9. Equivalence Relations and Canonical Forms of Matrices
4. 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
5. Linear Transformations
  1. Definitions
  2. Representation of Linear Transformations
  3. Representations Under Change of Bases
6. Eigenvalues and Eigenvectors
  1. Introduction
  2. Relation Between Eigenvalues and Minors
  3. Similarity
  4. Algebraic and Geometric Multiplicites
  5. Jordan Canonical Form
  6. Functions of Matrices
  7. Application: Markov Chains
7. 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. Central Conics and Quadrics
  7. The Natural Inverse
  8. Normal Matrices
8. 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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