product iamge

Linear Transformation: Examples and Solutions

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Download
Search on Amazon

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

This book introduces linear transformation and its key results, which have applications in engineering, physics, and various branches of mathematics. Linear transformation is a difficult subject for students.

This concise text provides an in-depth overview of linear trans-formation. It provides multiple-choice questions, covers enough examples for the reader to gain a clear understanding, and includes exact methods with specific shortcuts to reach solutions for particular problems.

Research scholars and students working in the fields of engineering, physics, and different branches of mathematics need to learn the concepts of linear transformation to solve their problems. This book will serve their need instead of having to use the more complex texts that contain more concepts then needed.

The chapters mainly discuss the definition of linear transformation, properties of linear transformation, linear operators, composition of two or more linear transformations, kernels and range of linear transformation, inverse transformation, one-to-one and onto transformation, isomorphism, matrix linear transformation, and similarity of two matrices.

Author(s): Nita H. Shah, Urmila B. Chaudhari
Series: Mathematical Engineering, Manufacturing, and Management Sciences
Publisher: CRC Press
Year: 2020

Language: English
Pages: 90
City: Boca Raton

Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgements
Authors
Chapter 1 Linear Transformations of Euclidean Vector Space
1.1 Linear Transformations from R[sup(n)] to R[sup(m)]
1.1.1 Transformations from R[sup(n)] to R[sup(m)]
1.1.2 Linear Transformations from R[sup(n)] to R[sup(m)]
1.2 Matrix Representation of Linear Transformations
1.3 Different Types of Operators and their Composition
1.3.1 Reflection Operator
1.3.2 Orthogonal Projection Operator
1.3.3 Rotation Operator
1.3.4 Contraction and Dilation Operators
1.3.5 Shear Operator
1.4 Composition of Two or More Transformations
Exercise Set 1
Answers to Exercise Set 1
Chapter 2 General Linear Transformations
2.1 Introduction of General Linear Transformations
2.1.1 Properties of Linear Transformations
2.2 Forming a Linear Transformation
2.2.1 Obtaining Linear Transformations from Basis Vectors and their Image Vectors
2.3 Kernel and Range of Linear Transformation T
2.4 Composition of the Linear Transformation
Exercise Set 2
Answers to Exercise Set 2
Chapter 3 Inverse Linear Transformation
3.1 One-One Transformation
3.1.1 Some Important Results
3.2 Onto Transformation
3.3 Isomorphism
3.4 Inverse Linear Transformation
Exercise Set 3
Answers to Exercise Set 3
Chapter 4 Matrices of General Linear Transformations
4.1 Matrix of General Transformations
4.2 Similarity
4.2.1 Effect of Changing Bases on Matrices of Linear Operators
Exercise Set 4
Answers to Exercise Set 4
Multiple-Choice Questions on Linear Transformation
Bibliography
Index