Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such...

Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) A = 5 0 0 0 1 3 0 3 1 (D, Q) = $$ Incorrect: Your answer is incorrect. Submission 2(0/1 points)Monday, November 25, 2019 10:01 PM CST Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) A = 5 0 0 0 1 3 0 3 1 (D, Q) = $$ Incorrect: Your answer is incorrect. Submission 3(0/1 points)Monday, November 25, 2019 10:08 PM CST Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) A = 5 0 0 0 1 3 0 3 1 (D, Q) = $$ Incorrect: Your answer is incorrect.

Expert Solution

Colby Messinger answered 2 years ago

Consider an orthogonal matrix Q ∈ R ^m×m and a diagonal matrix with non-zero diagonal elements...

Consider an orthogonal matrix Q ∈ R ^m×m and a diagonal matrix with non-zero diagonal elements D ∈ R^ m×m and answer the True— False questions below. (k) Any vector x ∈ R^m can be written as a linear combination of the columns of D (l) The columns of Q span R^m (m) The columns of D span R^m (n) The columns of Q are a basis for R^m (o) The columns of D are a basis for R^m

Diagonalize the matrix (That is, find a diagonal matrix D and an invertible matrix P such...

Diagonalize the matrix (That is, find a diagonal matrix D and an invertible matrix P such that A=PDP−1. (Do not find the inverse of P). Describe all eigenspaces of A and state the geometric and algebraic multiplicity of each eigenvalue. A= -1 3 0 -4 6 0 0 0 1

P.0.2 Show that (a) the diagonal entries of a Hermitian matrix are real; (b) the diagonal...

P.0.2 Show that (a) the diagonal entries of a Hermitian matrix are real; (b) the diagonal entries of a skew-Hermitian matrix purely imaginary; c) the diagonal entries of a skew-symmetric matrix are zero. P.0.5 Let A ∈ Mn be invertible. Use mathematical induction to prove that (A-1)k = (Ak)-1 for all integers k. P.0.25 Let A ∈ Mn be idempotent. Show that A is invertible if and only if A = I P.0.26 Let A,B ∈ Mn be idempotent. Show...

(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal...

(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix D such that P −1AP = D. Otherwise, explain why A is not diagonalizable. (a) A = −3 0 −5 0 2 0 2 0 3 (b) A = 2 0 −1 1 3 −1 2 0 5 (c) A = 1 −1 2 −1 1 2 2 2 2

For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal....

For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.) A = 2 −2 3 0 3 −2 0 −1 2 P = Verify that P−1AP is a diagonal matrix with the eigenvalues on the main diagonal. P−1AP =

Find an orthogonal matrix P that diagonalizes the following matrix A: A is 3 by 3...

Find an orthogonal matrix P that diagonalizes the following matrix A: A is 3 by 3 matrix: (3 1 0 1 -1 1 0 0 2)

Give an example of a square matrix A such that all the diagonal entries are positive...

Give an example of a square matrix A such that all the diagonal entries are positive but A is not positive definite

What are the eigenvalues and eigenvectors of a diagonal matrix? Justify your answer (explain) These questions...

What are the eigenvalues and eigenvectors of a diagonal matrix? Justify your answer (explain) These questions follow the exercises in Chapter 4 of the book, Scientic Computing: An Introduction, by Michael Heath. They study some of the properties of eigenvalues, eigenvectors, and some ways to compute them.

(a) Show that the diagonal entries of a positive definite matrix are positive numbers. (b) Show...

(a) Show that the diagonal entries of a positive definite matrix are positive numbers. (b) Show that if B is a nonsingular square matrix, then BTB is an SPD matrix.(Hint. you simply need to show the positive definiteness, which does requires the nonsingularity of B.)

Write a C# console program that fills the right to left diagonal of a square matrix...

Write a C# console program that fills the right to left diagonal of a square matrix with zeros, the lower-right triangle with -1s, and the upper left triangle with +1s. Let the user enter the size of the matrix up to size 21. Use a constant and error check. Output the formatted square matrix with appropriate values. Refer to the sample output below. Sample Run: *** Start of Matrix *** Enter the size of square (<= 21): 5 1 1...

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