Linear Algebra: UNIT II: Linear Transformations and Diagonalization

Linear Transformation and Diagonalization

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In the first module we dealt with theory of abstract vector spaces in detail. Now it is to consider those functions defined on vector spaces that in some sense preserve the structure.

Module − II

LINEAR TRANSFORMATION AND DIAGONALIZATION

INTRODUCTION

In the first module we dealt with theory of abstract vector spaces in detail. Now it is to consider those functions defined on vector spaces that in some sense preserve the structure. These special functions are called linear transformations and are widely used in pure and applied mathematics. The operations of differentiation and integration provide us with two of the most important examples of linear transformations. These two concepts provide us to reformulate many problems in differential and integral equations interms of linear transformations on vector spaces.

Linear Algebra: UNIT II: Linear Transformations and Diagonalization : Tag: maths, mathematics : - Linear Transformation and Diagonalization

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Linear Algebra: UNIT II: Linear Transformations and Diagonalization

Linear Transformation and Diagonalization

Definition and Properties of Linear Transformation

Linear Transformation: Example Solved Problems

Null space (or) Kernel N(T) and Range (or) Image R(T)

Null space (or) Kernel N(T) and Range (or) Image R(T): Example Solved Problems

Null space (or) Kernel N(T) and Range (or) Image R(T): Theorem Part 2

Null space (or) Kernel N(T) and Range (or) Image R(T): Example Solved Problems - Part 2

Linear Transformations: Projection

Linear Transformation: Example Solved Problems

Matrix Representation of a Linear Transformation

Matrix Representation of a Linear Transformation: Example Solved Problems

Matrix Representation of a Linear Transformation: Theorems

Matrix Representation of a Linear Transformation: Example Solved Problems Using Theorems

Definition of Diagonalizable, Eigenvalues and Eigenvector

Eigenvalues and Eigenvectors: Theorem 1

Eigenvalues and Eigenvectors: Theorem 1 - Example Solved Problems

Eigenvalues and Eigenvectors: Theorem 2

Eigenvalues and Eigenvectors: Theorem 2 - Example Solved Problems

Linear Transformations: Characteristic polynomial

Characteristic Polynomial: Example Solved Problems

Eigenvalues and Eigenvectors: Theorem 3

Eigenvalues and Eigenvectors: Theorem 3 - Example Solved Problems

Diagonalizability: Theorems Part 1

Diagonalizability: Theorems Part 1 - Example Solved Problems

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