-1 1 Question 4 (5 points). Let A = Find a singular value decomposition of A.
2 2 Let A = -1 -4 2 -4 UΣVT. (a) Find a singular value decomposition A (b) Determine the pseudoinverse matrix A+, expressing A+ as a single matrix.
4. (a) Find a singular value decomposition of A. (b) Based on the decomposition, find the following information of A . rank (A) An orthonormal basis of range(A) An orthonormal basis of null(A) An orthonormal basis of range(A) An orthonormal basis of null(AT) (c) Find an eigendecomposition of A and compare it with the singular value decomposition 4. (a) Find a singular value decomposition of A. (b) Based on the decomposition, find the following information of A . rank (A)...
1 -1 Let A= -1 -2 1 1 singular value decomposition A = U£VT (a) Find a (b) Determine the pseudoinverse matrix At, expressing At single matrix. as a (c) Consider the equation ) Ax 1 = and find the least squares approximation x' with minimum norm 1 -1 Let A= -1 -2 1 1 singular value decomposition A = U£VT (a) Find a (b) Determine the pseudoinverse matrix At, expressing At single matrix. as a (c) Consider the equation...
Let . (a) Find the singular value decomposition of A. (b) Find the least squares solution to the linear system We were unable to transcribe this imageWe were unable to transcribe this image
1. (25 points) (hand solution) Find the Singular Value Decomposition (SVD) of A. Use the reduced version if the situation allows it 42 0 1 0 2 2 when producing the SVD. order the values such that σ1-σ2 On 1. (25 points) (hand solution) Find the Singular Value Decomposition (SVD) of A. Use the reduced version if the situation allows it 42 0 1 0 2 2 when producing the SVD. order the values such that σ1-σ2 On
Homework problem: Singular Value Decomposition Let A E R n 2 mn. Consider the singular value decomposition A = UEVT. Let u , un), v(1),...,v(m), and oi,... ,ar denote the columns of U, the columns of V and the non-zero entries (the singular values) of E, respectively. Show that 1. ai,.,a are the nonzero eigenvalues of AAT and ATA, v(1)... , v(m) the eigenvectors of ATA and u1)...,un) (possibly corresponding to the eigenvalue 0) are the eigenvectors of AAT are...
8. Consider the real matrix As -1 0 (a) (3 pts) Find the singular values of A. (b) (4 pts) Find a singular value decomposition of A. (c) (3 pts) Find 8. Consider the real matrix As -1 0 (a) (3 pts) Find the singular values of A. (b) (4 pts) Find a singular value decomposition of A. (c) (3 pts) Find
4. Find the singular value decomposition of matrix 3 6 -3 -6 B 23 -4 17 -16
Use permutation matrices to find the singular value decomposition of the matrix 0 0 -3] A=| 0 +8 01. -5 00 Use permutation matrices to find the singular value decomposition of the matrix 0 0 -3] A=| 0 +8 01. -5 00
=[e - ] f,l which depends 3. (5 points each-10 points) Consider the rank one matrix A- on two real parameters e and f. (a) Find the singular value decomposition (SVD) A-υΣγί =[e - ] f,l which depends 3. (5 points each-10 points) Consider the rank one matrix A- on two real parameters e and f. (a) Find the singular value decomposition (SVD) A-υΣγί