Spectral decomposition

(1 mark each) For each of the given matrices, select all decompositions that can be applied to it. You do not have to show your work for this question. 2 ) A = [61 O Diagonalization (i.e., A = PDP-1 with D diagonal) O Schur triangularization O Spectral decomposition O Singular value decomposition b ) B = 0 1.001 Diagonalization O Schur triangularization O Spectral decomposition Singular value decomposition c) C is the 75 x 75 matrix with every entry equal to 1. Diagonalization Schur triangularization O Spectral decomposition Singular value decomposition d) D = 0 1 1 Diagonalization OSchur triangularization Spectral decomposition Singular value decomposition2. Spectral Versus Singular Value Decomposition: Consider a linear operator A with matrix representation 1 3 A _ [7 _1] (a) Compute the spectral decomposition and singular 1mlue decomposition of A. (1:) Sketch ANSI}, the image of the unit circle under .A. (c) Compare your answers to parts (a) and {b} and draw a conclusion. Question 4 Let 1 A = -1 1 1 -1 (a) Calculate A A and find its spectral decomposition. (b) Calculate AA and find its spectral decomposition. (c) Compare the nonzero eigenvalues of A A and those of AAT.Find the spectral decomposition of es . A = 0 0 1+ Write each orthogonal projection matrix as a single matrix