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Problem 3 (20 points): The covariance matrix of a random signal is: 13 6 (1) Find...
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3 Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0...
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
The covariance matrix of an image with three spectral components is shown below. Find the first principal component of...
The covariance matrix of an image with three spectral components is shown below. Find the first principal component of the data, and compute the percentage of the total variance that is contained in this component. Use technology with matrix capabilities to help solve this problem 167.58 27.09 79.95 S27.09 563.36 253.21 79.95 253.21 205.49 What is the first principal component of the data? Choose the correct answer below. Note that technology may output the negative of first principal component, but...
Problem 1. (2 points) Find a 2 x 2 matrix A such that [-] and are...
Problem 1. (2 points) Find a 2 x 2 matrix A such that [-] and are eigenvectors of A with eigenvalues 9 and 3, respectively. A=
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3. 2. Use...
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
(20=10+5+5 points) Let 2 1 1] A = 1 2 1 . 11 1 2 (a)...
(20=10+5+5 points) Let 2 1 1] A = 1 2 1 . 11 1 2 (a) Find the spectral decomposition of A, i.e., represent it as a linear combination of projection matrices with eigenvalues of A as coefficients. (b) How many matrices B exist such that B2 = A? (c) Calculate one of such matrix.
Problem 5. (20 points) 1) Find all the eigenvalues of the matrix A SE 1 2...
Problem 5. (20 points) 1) Find all the eigenvalues of the matrix A SE 1 2 31 2) Find all the eigenvalues of the matrix A = [32]
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix (3 2 6 1...
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix (3 2 6 1 -2 3 16 12 b) Find the Fourier series representation of the function with period 2 given by +2 ost < ist <2x f(t) = {. 2 ºs!<
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1...
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1 -2 3 L6 4 12 b) Find the Fourier series representation of the function with period 21 given by t2 0 <t<TE i < t < 270 f(t) = {.
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6...
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
6. (20') Given the 3 x 3 matrix A= 0 0 1 0 2 0 4...
6. (20') Given the 3 x 3 matrix A= 0 0 1 0 2 0 4 0 0 (a) compute ATA. (b) find all eigenvalues of ATA and their associated eigenvectors. (c) write down all singular values of A in descending order. (d) find the singular-value decomposition(SVD) A = UEVT. (e) based on the above calculation, write down the SVD for the following matrix B. (You can certainly perform all the work again if you have sufficient time but do...
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
The covariance matrix of an image with three spectral components is shown below. Find the first principal component of the data, and compute the percentage of the total variance that is contained in this component. Use technology with matrix capabilities to help solve this problem 167.58 27.09 79.95 S27.09 563.36 253.21 79.95 253.21 205.49 What is the first principal component of the data? Choose the correct answer below. Note that technology may output the negative of first principal component, but...
Problem 1. (2 points) Find a 2 x 2 matrix A such that [-] and are eigenvectors of A with eigenvalues 9 and 3, respectively. A=
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
2. Use the spectral decomposition (in reverse) to find the matrix A such that (1,-1,1) is an eigenvector with eigenvalue 2, and (2, 3, 1) and (4,-1,5) are eigenvectors with eigenvalue-3.
(20=10+5+5 points) Let 2 1 1] A = 1 2 1 . 11 1 2 (a) Find the spectral decomposition of A, i.e., represent it as a linear combination of projection matrices with eigenvalues of A as coefficients. (b) How many matrices B exist such that B2 = A? (c) Calculate one of such matrix.
Problem 5. (20 points) 1) Find all the eigenvalues of the matrix A SE 1 2 31 2) Find all the eigenvalues of the matrix A = [32]
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix (3 2 6 1 -2 3 16 12 b) Find the Fourier series representation of the function with period 2 given by +2 ost < ist <2x f(t) = {. 2 ºs!<
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1 -2 3 L6 4 12 b) Find the Fourier series representation of the function with period 21 given by t2 0 <t<TE i < t < 270 f(t) = {.
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
6. (20') Given the 3 x 3 matrix A= 0 0 1 0 2 0 4 0 0 (a) compute ATA. (b) find all eigenvalues of ATA and their associated eigenvectors. (c) write down all singular values of A in descending order. (d) find the singular-value decomposition(SVD) A = UEVT. (e) based on the above calculation, write down the SVD for the following matrix B. (You can certainly perform all the work again if you have sufficient time but do...
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