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(b) Let A = Find (i) an orthogonal basis for R? consisting of eigenvectors of A. (ii) an orthogonal matrix P and a diagonal matrix D such that A = PDPT.

(b) Let A = Find (i) an orthogonal basis for R? consisting of eigenvectors of A. (ii) an orthogonal matrix P and a diagonal matrix D such that A = PDPT.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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(a) Determine if the following statements are true or false. Prove if it is true or give counter example if it is false. Let T be the linear operator on inner product space C2. (i) T(x,y) = (2ix+3y,x– y) then T is self-adjoint. If W is an orthogonal set consisting non-zero vectors in R', then W is If (ii) linearly independent. If S and T are self-adjoint operators, ST + TS is also a self-adjoint operator. (ii) (b) Let A = Find (i) an orthogonal basis for R? consisting of eigenvectors of A. (ii) an orthogonal matrix P and a diagonal matrix D such that A = PDP" .
Transcribed Image Text:(a) Determine if the following statements are true or false. Prove if it is true or give counter example if it is false. Let T be the linear operator on inner product space C2. (i) T(x,y) = (2ix+3y,x– y) then T is self-adjoint. If W is an orthogonal set consisting non-zero vectors in R', then W is If (ii) linearly independent. If S and T are self-adjoint operators, ST + TS is also a self-adjoint operator. (ii) (b) Let A = Find (i) an orthogonal basis for R? consisting of eigenvectors of A. (ii) an orthogonal matrix P and a diagonal matrix D such that A = PDP" .
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