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8) Suppose V is finite-dimensional, T E L(V) had dim V distinct eigenvalues, and S E L(V) has the same eigenvectors as T (not necessarily with the same eigenvalues). Prove that ST = TS.

8) Suppose V is finite-dimensional, T E L(V) had dim V distinct eigenvalues, and S E L(V) has the same eigenvectors as T (not necessarily with the same eigenvalues). Prove that ST = TS.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 11AEXP
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8) Suppose V is finite-dimensional, T e L(V) had dim V distinct eigenvalues, and S e L(V) has the same eigenvectors as T (not necessarily with the same eigenvalues). Prove that ST = TS. 9) Suppose V is finite-dimensional and T E L(V). Let 1, ...,Am denote the distinct nonzero
Transcribed Image Text:8) Suppose V is finite-dimensional, T e L(V) had dim V distinct eigenvalues, and S e L(V) has the same eigenvectors as T (not necessarily with the same eigenvalues). Prove that ST = TS. 9) Suppose V is finite-dimensional and T E L(V). Let 1, ...,Am denote the distinct nonzero
Expert Solution
Step 1

As given by the question

There are given that the v is finite-dimensional.

And,

The distinct eigenvalues is:

T∈Lv

And,

The eigenvectors is:

S∈Lv

 

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