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Matrices & Linear Algebra on Advance 2ND Edition

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Matrices & Linear Algebra on Advance 2ND Edition Cover

 

Synopses & Reviews

Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.

Publisher Comments:

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.

Synopsis:

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.

Synopsis:

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.

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

Product Details

ISBN:
9780486660141
Other:
Schneider, Hans
Publisher:
Dover Publications
Author:
Schneider, Hans
Author:
Mathematics
Author:
Barker, George Phillip
Author:
Hans Schneid
Author:
er
Subject:
Algebra - General
Subject:
Algebra - Linear
Subject:
Algebras, linear
Subject:
Matrices
Subject:
General Mathematics
Subject:
Mathematics - Algebra
Edition Number:
2
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19890631
Binding:
TRADE PAPER
Language:
English
Pages:
432
Dimensions:
8.5 x 5.38 in 1 lb

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Matrices & Linear Algebra on Advance 2ND Edition Used Trade Paper
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Product details 432 pages Dover Publications - English 9780486660141 Reviews:
"Synopsis" by ,
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.

"Synopsis" by ,
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.

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