Linear Transformation

Examples and Solutions

Nita H. Shah, Urmila B. Chaudhari

• Editorial: CRC Press
• Año: 2020
• ISBN:
  9781000337440
• Edición: 1
• Categoría: Mathematik
• Categoría: Angewandte Mathematik

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.

1 Linear Transformations of Euclidean Vector Space

In this chapter, we will start with the study about the function of the form $w=f\left(X\right)$, where $X$ is the independent vector in $R^n$ and $w$ is a dependent variable in $R^m$. We will concentrate on a special case as the transformation from $R^n$ to $R^m$. A linear transformation is fundamental in the study of linear algebra. Hence, we will study linear transformation and different types of operators such as reflection operator, orthogonal projection operator, rotation operator, dilation operator, contraction operator, and shear operator. Many applications are related to the operator in the field of physi...