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Matrices and Linear Algebra : Dover Books on Advanced Mathematics - HANS SCHNEIDER

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Matrices and Linear Algebra

By: HANS SCHNEIDER

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Paperback | 1 June 1989 | Edition Number 2

At a Glance

Paperback
432 Pages

Edition Type
New edition

Dimensions(cm)
20.9 x 13.6 x 2.54

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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. Includes numerous exercises. Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it. This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations. Table of Contents: l. The Algebra of Matrices 2. Linear Equations 3. Vector Spaces 4. Determinants 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Inner Product Spaces 8. Applications to Differential Equations For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Religion & Beliefs

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
Bases and Representations
Row Spaces of Matrices
Column Equivalence
Row-Column Equivalence
Equivalence Relations and Canonical Forms of Matrices
Determinants
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
Definitions
Representation of Linear Transformations
Representations Under Change of Bases
Eigenvalues and Eigenvectors
Introduction
Relation Between Eigenvalues and Minors
Similarity
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
Introduction
Homogeneous Differential Equations
Linear Differrential Equations: The Unrestricted Case
Linear Operators: The Global Vie?
Answers
Symbols
Index
Table of Contents provided by Publisher. All Rights Reserved.

Matrices and Linear Algebra

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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