EL ENG 127 Midterm: ee127-sp2009-mt1-El Ghaoui-soln
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The exam is open notes, but access to the internet is not allowed. When asked to prove something, do not merely take an example; provide a rigorous proof with clear steps. Also, some parts are more di cult than others and you are not expected to nish the exam: (2 points) show that the frobenius norm of a matrix a depends only on its singular values. Precisely, show that kakf = k k2, where := ( 1, . , r) is the vector formed with the singular values of a, and r is the rank of a. Assume a rm n: by re-writing this in terms of the squared frobenius norm, kak2. 2 , the sum going to r because only the rst r eigenvalues of a are non-zero: we can use the svd of a = u v t , with = diag( 1, .
