Linear Algebra 1st editon by Shen, Haohao Wang, Wojdylo ISBN 1683923766 978-1683923763

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Product details:

ISBN 10: 1683923766
ISBN 13: 978-1683923763
Author:  L. Shen, Haohao Wang, J. Wojdylo

The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester coursein linear algebra that can be used in a variety of contexts. The presentationof the material combines definitions and proofs with an emphasis oncomputational applications, providing examples that illustrate the use ofsoftware packages such as Mathematica^®,Maple^®, and Sage.

Features:

– Introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications

– Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields.

Linear Algebra 1st Table of contents:

Chapter 1 Vector Spaces

1.1 Vector Spaces

1.2 Linear Span and Linearly Independence

1.3 Bases for Vector Spaces

1.4 Linear System of Equations

1.5 A First Look of Determinants

1.6 Using Computer Algebra Systems to Perform Computations

1.7 Applications of Vector Spaces

1.7.1 Code

1.7.2 Hamming Code

1.7.3 Linear Code

1.7.4 Golay Code

1.8 Exercises

Chapter 2 Linear Transformations

2.1 Linear Transformations

2.2 Rank and Nullity of a Linear Transformation

2.3 Representation of Linear Transformations by Matrices

2.4 The Algebra of Linear Transformation

2.5 Applications of Linear Transformation

2.5.1 Affine Transformations

2.5.2 Projective Transformations

2.6 Exercises

Chapter 3 Linear Operators

3.1 Characteristic and Minimal Polynomials

3.2 Eigenspaces and Diagonalizability

3.3 Jordan Canonical Form

3.4 Trace

3.5 Determinants

3.6 Generalized Companion Matrix

3.7 Solution of Linear System of Equations

3.8 Some Applications of Matrices

3.8.1 Linear Programming

3.8.2 Geometric Transformation

3.8.3 Matrices in Graph Theory

3.8.4 Positional Relationship of Two Ellipsoids

3.9 Exercises

Chapter 4 Orthogonal Bases

4.1 Inner Product Spaces

4.2 Gram-Schmidt Process to Produce Orthonormal Basis

4.3 Orthogonal Complements and Projections

4.4 Orthogonal Projections and Reflections

4.4.1 Orthogonal Projection Matrix

4.4.2 Reflection Matrix

4.5 Properties of Symmetric Matrices

4.6 QR Factorization

4.7 Singular Value Decomposition

4.8 Applications of SVD and QR Decompositions

4.8.1 Image Processing

4.8.2 QR decomposition and GCD

4.9 Exercises

Chapter 5 Matrix Decomposition

5.1 Decomposition over R or C

5.1.1 Decompositions to Solve Linear Systems

5.1.2 Decompositions Based on Eigenvalues

5.1.3 Examples

5.2 Iterative Methods to Solve Linear Systems Numerically

5.2.1 Jacobi Iterative Method

5.2.2 Gauss-Seidel Iterative Method

5.3 Matrix over Principle Ideal Domain

5.3.1 Matrix Decomposition over PID

5.4 Exercises

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