Question

LINEAR ALGEBRA: Sheldon Axler, “Linear Algebra Done Right”

I only need the table completed with answers either (always true , sometimes, or no ) and short explanation if sometimes.

3, Let T e L(V), and 'B be an orthonormal basis, so that (5+20 pts) Is T self-adjoint? Why/Why Not? (5+20 pts) Is T normal? Why/Why Not? (10 pts/box with explanation) Now, let RE C(V) be a self-adjoint operator, SEL(V) a normal operator, and U E C(V) an operator that is neither self-adjoint nor normal; what properties do these operators have-mark R (if true only for F = R) / C (if true only for F-C) / F (always true no sometimes): U,Neither op = R. S.orU 1 R, Self Adjoint S, Normal (Not Self-Adjoint) 3 ortho-normal basis: M(op, B) is upper triangular 3 ortho-normal basis: M(op, 28) is diagonal all eigenvalues of op are real --TIr op has positive square root op has polar decomposition op has singular value decomposition On the next page (not in the boxes!!for each answer in the grid give a SHORT EXPLANA- TION (why/why not, or what is the "extra condition(s) needed for the "sometimes" properties?

Answer 1

5 5 5 1 500 O o agona