Homework Answers
16 ..
here A is orthogonal matrix .. then it is already in singular value decomposotiion form ..
so all its singular values = 1 ...
yes SVD of orthogonal matrix is unique ....
any doubt in this then comment below .. i will explain you
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16. (a) Suppose that A is an orthogonal matrix. What are its singular values? (b) Is...
9. a) Suppose that A is an orthogonal matrix. What are its singular values? b) Is...
9. a) Suppose that A is an orthogonal matrix. What are its singular values? b) Is the SVD of a given matrix A unique in general?
υΣνΤ. Answer the following questions: Suppose a matrix A E Rmxn has an SVD A (i) Show that the rank of the miatrix A E Rmxn is equal to the number of its nonzero singular values. (ii) Show that miult...
υΣνΤ. Answer the following questions: Suppose a matrix A E Rmxn has an SVD A (i) Show that the rank of the miatrix A E Rmxn is equal to the number of its nonzero singular values. (ii) Show that miultiplication by an orthogonal matrix on the left and multiplication by an orthogonal matrix on the right, i.e., UA and BU, where A E Rmxn and B ERnm are general matrices, and U Rxm is an orthogonal matrix, preserve the Frobenius...
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...
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...
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 (usi...
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)...
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...
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) Suppose A = UEVT is a singular value decomposition for A. The nxm matrix At...
(4) Suppose A = UEVT is a singular value decomposition for A. The nxm matrix At = VETUT where st is defined in (1g) is called a pseudoinverse of A. Let x = Atb. (a) Show that x satisfies the equation AAx = A'b and conclude that x is a least squares solution to Ax = b. (b) Show that x = Alb lies in row(A) and conclude that x = projrow(A)(x). (c) Conclude that x is the smallest least...
6. (20") Given the 3 x 3 matrix A- 20 00 (a) compute A'A. (b) find...
6. (20") Given the 3 x 3 matrix A- 20 00 (a) compute A'A. (b) find all eigenvalues of AA and their associated eigenwectors (c) write down all singular values of A in descending order (d) find the singular-value decomposition(SVD) A-UEV"
QUESTION 11 A Find the singular values of the matrix. - 4 0 02 O A...
QUESTION 11 A Find the singular values of the matrix. - 4 0 02 O A 16,-2. OB 16,4 Oc 4,2 OD.-16,4 OE-4,2
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 p...
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
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 percentag...
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
9. a) Suppose that A is an orthogonal matrix. What are its singular values? b) Is the SVD of a given matrix A unique in general?
υΣνΤ. Answer the following questions: Suppose a matrix A E Rmxn has an SVD A (i) Show that the rank of the miatrix A E Rmxn is equal to the number of its nonzero singular values. (ii) Show that miultiplication by an orthogonal matrix on the left and multiplication by an orthogonal matrix on the right, i.e., UA and BU, where A E Rmxn and B ERnm are general matrices, and U Rxm is an orthogonal matrix, preserve the Frobenius...
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...
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)...
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) Suppose A = UEVT is a singular value decomposition for A. The nxm matrix At = VETUT where st is defined in (1g) is called a pseudoinverse of A. Let x = Atb. (a) Show that x satisfies the equation AAx = A'b and conclude that x is a least squares solution to Ax = b. (b) Show that x = Alb lies in row(A) and conclude that x = projrow(A)(x). (c) Conclude that x is the smallest least...
6. (20") Given the 3 x 3 matrix A- 20 00 (a) compute A'A. (b) find all eigenvalues of AA and their associated eigenwectors (c) write down all singular values of A in descending order (d) find the singular-value decomposition(SVD) A-UEV"
QUESTION 11 A Find the singular values of the matrix. - 4 0 02 O A 16,-2. OB 16,4 Oc 4,2 OD.-16,4 OE-4,2
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
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
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