A First Course in Linear Algebra - 1st Edition - ISBN: 9781483229560, 9781483265001

A First Course in Linear Algebra

1st Edition

Authors: Daniel Zelinsky
Editors: Samuel S. Saslaw
eBook ISBN: 9781483265001
Imprint: Academic Press
Published Date: 1st January 1968
Page Count: 276
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A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations.

This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem.

This publication is suitable for college students taking a course in linear algebra.

Table of Contents

1. Vectors

1. Coordinate Systems

2. Vectors and Their Components

3. Length of a Vector

4. Multiplication of Vectors by Scahrs

5. Addition of Vectors; Linear Combinations

6. Dot Products

7. Cross Products

8, Vectors in n-Space

9. Still More General Vector Spaces

2. Planes and Lines

1. Planes

2. Lines

3. Vector Functions of Scalars

3. Linear Functions

1. Definition

2. Matrices

3. Sums and Scalar Multiples of Linear Mappings

4. Composites of Linear Mappings and Products of Matrices

5. Inverses

6. Kernel and Image

4. Solution of Equations

1 Solution Process; Reduction to Echelon Form

2, Closer Analysis of the Solutions and the Solution Method

5. Dimension

1. Subspaces

2. Dimension

3. Rank

6. Determinants and Transposes

1. Computation of Determinants

2. Explicit Formulas

3. Transposes

4. Symmetric Matrices and Mappings

7. Eigenvalues

1. Diagonalizable Transformations

2. Computation of Eigenvalues and Eigenvectors

3. Principal Axis Theorem

8. Quadratic Forms and Change of Basis

1. Quadratic Forms

2. Change of Coordinates

3. Effect of Change of Basis on Matrices of Linear Functions

Appendix I. A Smattering of Logic

Appendix II. Existencc of Real Eigenvalues of Symmetric





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© Academic Press 1968
Academic Press
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About the Author

Daniel Zelinsky

About the Editor

Samuel S. Saslaw

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