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b.) If T € L(V) is self adjoint and UCV is a T-invariant subspace, then U is T-invariant. c.) If T € L(V) is diagonalizable, then V = ker(T) © Im(T). d.) If T is a positive operator, and λ = 4 is an eigenvalue of T2, then λ = 2 is an eigenvalue of T.

b.) If T € L(V) is self adjoint and UCV is a T-invariant subspace, then U is T-invariant. c.) If T € L(V) is diagonalizable, then V = ker(T) © Im(T). d.) If T is a positive operator, and λ = 4 is an eigenvalue of T2, then λ = 2 is an eigenvalue of T.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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this 3 statement is True， please give a proof 

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b.) If T = L(V) is self adjoint and U CV is a T-invariant subspace, then U is T-invariant. c.) If T € L(V) is diagonalizable, then V = ker(T) © Im(T). d.) If T is a positive operator, and of T. = 4 is an eigenvalue of T², then λ = 2 is an eigenvalue
Transcribed Image Text:b.) If T = L(V) is self adjoint and U CV is a T-invariant subspace, then U is T-invariant. c.) If T € L(V) is diagonalizable, then V = ker(T) © Im(T). d.) If T is a positive operator, and of T. = 4 is an eigenvalue of T², then λ = 2 is an eigenvalue
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