If is a singular value decomposition for a matrix , then is an orthogonal diagonalizing matrix for .

Question

If  is a singular value decomposition for a matrix  , then  is an orthogonal diagonalizing matrix for  .

Quizplus · Accepted Answer

By definition, the singular value decomposition of a matrix is given by A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix. Therefore, 11edaba5_20a2_ff96_a975_97693f3dd49f_TBMC1039_00 represents the singular values of the original matrix in diagonal form. If we multiply U and V^T, we obtain an orthogonal matrix that diagonalizes the original matrix, and this matrix is represented by 11edaba5_20a2_ff98_a975_efb49f44779b_TBMC1039_00. Therefore, the statement is true.

If Is a Singular Value Decomposition for a Matrix