The matrix be the linear transformation whose matrix with respect to the standard basis...
Posted: Tue Aug 03, 2021 12:14 pm
The matrix Let T\in \pounds (\mathbb{R}^{2}) be the linear transformation whose matrix with respect to the standard basis is cc{M}(T) = ((1,2),(3,4)) = A.
(a.) Calculate A^{*}A=V^{T}\Lambda V where ? is the diagonal matrix of eigenvalues of T*T with the largest eigenvalue in the first row and first column, and V is the matrix of eigenvectors of T*T.
(b.) Find the diagonal matrix ? of singular values of T.
(c.) The matrix A can be written in the form A=U?V where U is an isometry. Find U. (It is enough to express U as a product of specific matrices.)
(a.) Calculate A^{*}A=V^{T}\Lambda V where ? is the diagonal matrix of eigenvalues of T*T with the largest eigenvalue in the first row and first column, and V is the matrix of eigenvectors of T*T.
(b.) Find the diagonal matrix ? of singular values of T.
(c.) The matrix A can be written in the form A=U?V where U is an isometry. Find U. (It is enough to express U as a product of specific matrices.)
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