1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint...

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1. Let $T$ be the operator on $\mathbb{F}^2$ whose matrix with respect to the standard basis is $(3 2) 2 -3$ .

a) Verify the result of proof " $T$ is normal if and only if $\left \| Tv \right \|=\left \| T^{*}v \right \|$ for all $v\in V$ " for question 1. Note: $T^{*}$ stands for adjoint

b) Verify the result of proof "Orthogonal eigenvectors for normal operators" for question 1. The proof states suppose $TE L(V)$ is normal then eigenvectors of $T$ corresponding to distinct eigenvalues are orthogonal.

(3 2) 2 -3

TE L(V)

math Advanced-Math

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Answer 1

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1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint...