=[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 de...
3. Consider the following 3 × 2 matrix: Го -2 0 (a) (By hand.) Find the singular value decomposition (SVD) of A. (b) (By hand.) Find the outer product form of the SVD of A. c) (By hand.) Compute (using singular values) A 2 3. Consider the following 3 × 2 matrix: Го -2 0 (a) (By hand.) Find the singular value decomposition (SVD) of A. (b) (By hand.) Find the outer product form of the SVD of A. c)...
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
d,e,f and g please Exercise (5.3). Consider the matriz A=/-211 -10 5 (a) Determine on paper a real SVD of A in the form A = UΣVT. The SVD is not unique, so find the one that has the minimal number of minus signs in U and V (b) List the singular values, left singular vectors, and right singular vectors of A. Draw a careful, labeled pic- ture of the unit ball in R2 and its image under A, together...
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
True or False? 1. If σ is a singular value of a matrix A, then σ is an eigenvalue of ATA Answer: 2. Every matrix has the same singular values as its transpose Answer: 3. A matrix has a pseudo-inverse if and only if it is not invertible. Answer: 4. If matrix A has rank k, then A has k singular values Answer:_ 5. Every matrix has a singular value decomposit ion Answer:_ 6. Every matrix has a unique singular...
Consider the data matrix (A) Center the data. (B) Find the SVD for the centered A. (C) Compute A', obtained by replacing the smallest singular value in Σ by 0. ' (D) What percentage of the total variance of A is preserved by A'? 3 21 A= 1 0-2 (A) Center the data. (B) Find the SVD for the centered A. (C) Compute A', obtained by replacing the smallest singular value in Σ by 0. ' (D) What percentage of...
(4) The following is the singular value decomposition of a 3 x 4 matrix A with some entries not given 1/3 -2/V5 1/v5 2/3 2/3 3 0 12/13 5/13 3/5 4/5 5/13 12/13 0 0 A 0 2 0 0 0 0 0 0 0 (a) What are the eigenvalues of AAT? of ATA? What is the rank of A? 1 2 (b) Find a non-zero vector w such that AAT = 9w. such that ATAu 4u. (c) Find a...
IV. Let (10 pts) A= TO0] 4 0 , [ 00] B= 54 0] 3 5. [55] a) Give the reduced SVD decomposition of the matrix A. b) Give the full SVD decomposition of the matrix A. c) Show that 01 = 90 is a singular value of B and find any other singular values if they exist. d) Show that vi = is an eigenvector of B* B corresponding to the singular value 01. e) Give the reduced SVD...
Consider the data matrix in the photo. (A) Center the data. (B) Find the SVD for the centered A. (C) Compute A’ , obtained by replacing the smallest singular value in Σ by 0. ′ (D) What percentage of the total variance of A is preserved by A’ ? 3 21 A= 1 0-2 3 21 A= 1 0-2
(5) Consider the 3 x 3 matrix A = 1-ovyT where the vector E R, 1 is the identity matrix and v (a) Determine the eigenvalues and eigenvectors of A. b) Hence find a matrix which diagonalises A. c) For which a is the matrix A singular? (d) For which a is the matrix A orthogonal ? (5) Consider the 3 x 3 matrix A = 1-ovyT where the vector E R, 1 is the identity matrix and v (a)...