In a singular value decomposition of matrix A - V = 0.5 -0.71 0.41 -0.5 -0.5 0.5 U = 0.0 0.0 0.82 -0.71 0.0 0.0 0.71 0.71 0.41 0.0 Ex: 1.23 60 -3 -3 07 %] -3 -3 6] what is U? with Σ = 8.49 0 0 6.0 00 00 and
In a singular value decomposition of matrix A - V = 0.5 -0.71 0.41 -0.5 -0.5 0.5 U = 0.0 0.0 0.82 -0.71 0.0 0.0 0.71 0.71 0.41 0.0 Ex: 1.23 60 -3 -3 07 %] -3 -3 6] what is U? with Σ = 8.49 0 0 6.0 00 00 and
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![In a singular value decomposition of matrix \( A = \begin{bmatrix} 6 & -3 & -3 & 0 \\ 0 & -3 & -3 & 6 \end{bmatrix} \) with \( \Sigma = \begin{bmatrix} 8.49 & 0 & 0 & 0 \\ 0 & 6.0 & 0 & 0 \end{bmatrix} \) and
\[ V = \begin{bmatrix} 0.5 & -0.71 & 0.41 & 0.0 \\ -0.5 & 0.0 & 0.82 & -0.71 \\ -0.5 & 0.0 & 0.0 & 0.71 \\ 0.5 & 0.71 & 0.41 & 0.0 \end{bmatrix} \]
what is \( U \)?
This exercise demonstrates the concept of singular value decomposition (SVD), where:
- \( A \) is the original matrix,
- \( \Sigma \) (Sigma) is the diagonal matrix of singular values,
- \( V \) is the matrix of right singular vectors,
- \( U \) is the matrix of left singular vectors to be determined.
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Note: There is a placeholder for users to input or calculate the matrix \( U \):
\[ U = \begin{bmatrix} \text{Ex: 1.23} & \\ & \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97fa71a9-ddb9-496b-9b0a-bf970e388fad%2Ff183e724-9b23-423f-a21c-092fdf52f088%2Fxcpgfem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In a singular value decomposition of matrix \( A = \begin{bmatrix} 6 & -3 & -3 & 0 \\ 0 & -3 & -3 & 6 \end{bmatrix} \) with \( \Sigma = \begin{bmatrix} 8.49 & 0 & 0 & 0 \\ 0 & 6.0 & 0 & 0 \end{bmatrix} \) and
\[ V = \begin{bmatrix} 0.5 & -0.71 & 0.41 & 0.0 \\ -0.5 & 0.0 & 0.82 & -0.71 \\ -0.5 & 0.0 & 0.0 & 0.71 \\ 0.5 & 0.71 & 0.41 & 0.0 \end{bmatrix} \]
what is \( U \)?
This exercise demonstrates the concept of singular value decomposition (SVD), where:
- \( A \) is the original matrix,
- \( \Sigma \) (Sigma) is the diagonal matrix of singular values,
- \( V \) is the matrix of right singular vectors,
- \( U \) is the matrix of left singular vectors to be determined.
---
Note: There is a placeholder for users to input or calculate the matrix \( U \):
\[ U = \begin{bmatrix} \text{Ex: 1.23} & \\ & \end{bmatrix} \]
Expert Solution
Step 1: Definition
The singular value decomposition of a matrix A of order m×n is defined as
U is a m×m matrix of orthonormal eigenvectors of AAT .
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