9780199654444

Linear Algebra: Step by Step

Kuldeep Singh

1st Edition

Linear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google sear

1-1

Systems of Linear Equations

Exercises

p.11

1-2

Gaussian Elimination

Exercises

p.26

1-3

Vector Arithmetic

Exercises

p.39

1-4

Arithmetic of Matrices

Exercises

p.55

1-5

Matrix Algebra

Exercises

p.73

1-6

The Transpose and Inverse of a Matrix

Exercises

p.89

1-7

Types of Solutions

Exercises

p.103

1-8

The Inverse Matrix Method

Exercises

p.118

Miscellaneous Exercises

p.120

3-1

Introduction to General Vector Spaces

Exercises

p.201

3-2

Subspace of a Vector Space

Exercises

p.214

3-3

Linear Independence and Basis

Exercises

p.227

3-4

Dimension

Exercises

p.238

3-5

Properties of a Matrix

Exercises

p.252

3-6

Linear Systems Revisited

Exercises

p.267

Miscellaneous Exercises

p.269

5-1

Introduction to Linear Transformations

Exercises

p.350

5-2

Kernel and Range of a Linear Transformation

Exercises

p.362

5-3

Rank and Nullity

Exercises

p.371

5-4

Inverse Linear Transformations

Exercises

p.387

5-5

The Matrix of a Linear Transformation

Exercises

p.403

5-6

Composition and Inverse Linear Transformations

Exercises

p.419

Miscellaneous Exercises

p.422

7-1

Introduction to Eigenvalues and Eigenvectors

Exercises

p.503

7-2

Properties of Eigenvalues and Eigenvectors

Exercises

p.517

7-3

Diagonalization

Exercises

p.531

7-4

Diagonalization of Symmetric Matrices

Exercises

p.547

7-5

Singular value Decomposition

Exercises

p.560

Miscellaneous Exercises

p.560