Consider the spaces V = R and W = Rm equipped with the Euclidean norms. Suppose...

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Consider the spaces V = R" and W = Rm equipped with the Euclidean norms. Suppose T = L(R", Rm has the matrix representation T = [a]. Define Show that m n · ΣΣ i=1 j=1 ||T||2 := ||TT||2 ≤ ||T||2||||2, TER". Consider the spaces V = R" and W = Rm equipped with the Euclidean norms. Suppose T = L(R", Rm has the matrix representation T = [a]. Define Show that m n · ΣΣ i=1 j=1 ||T||2 := ||TT||2 ≤ ||T||2||||2, TER".

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The statement we need to prove is that the norm of Tx with respect to the Euclidean norm is less tha... View the full answer