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Linear transformation : examples and solutions /

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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 mult...

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Bibliographic Details
Main Authors: Shah, Nita H. (Author), Chaudhari, Urmila B. (Author)
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: Boca Raton : CRC Press, 2021.
Edition:First edition.
Series:Mathematical engineering, manufacturing, and management sciences
Subjects:
Algebras, Linear > Problems, exercises, etc.
Linear operators.
MATHEMATICS / Applied
TECHNOLOGY / Operations Research
BUSINESS & ECONOMICS / Operations Research
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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