Question: Q5. Let w, w ER and define A = vw. Prove that ||A||2 ||2||||2. Is the same result true for the Frobenius norm, ie. is

Q5. Let w, w ER" and define A = vw". Prove that ||A||2 ||2||||2. Is the same result true for the Frobenius norm, ie. is AF = P Prove this or give a counterexample. Hint: For the first part, figure out the rank and the SVD of A. For the second part: Use that the Frobenius norm can be written in terms of singular values. Let A=VWT rank (4)=1 Q5. Let w, w ER" and define A = vw". Prove that ||A||2 ||2||||2. Is the same result true for the Frobenius norm, ie. is AF = P Prove this or give a counterexample. Hint: For the first part, figure out the rank and the SVD of A. For the second part: Use that the Frobenius norm can be written in terms of singular values. Let A=VWT rank (4)=1

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