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there are 4 questions in this pic, for linear algebra

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norm of U). Suppose U E M, is unitary. Show that | | UllF = vn (here ||U|F is the Frobenius Suppose {v} C C" is an orthonormal basis of C". Show that 72 Vivi = I. i=1

. Let A, B E MAR) and suppose that A = AT and B = —BT_ Prove that {31,3} = D, where (-, -) is the Frobenius inner product on M."(R). _ I The statement analogous to part (b) is not true in MAC). Find A, B E MAC) satisfying A = A" and B = —B*, but which have {11,3} 7': D.

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