3 A = 4
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
Find an SVD of the indicated matrix.
Expert Solution
Step 1
Let
To find singular value decomposition (SVD) of
The singular value decomposition of a matrix is factorization of matrix into the product of three matrices.
First find transpose of matrix .
Step 2
Consider
Now find the eigenvalues and eigenvectors of .
For that consider .
Now we will find eigenvectors corresponding to each eigenvalue.
For
Consider
Perform
Here
To find the null space solve the matrix equation .
If we take then .
Thus eigenvector corresponding to eigenvalue is
For
Consider
Perform
Here
To find the null space solve the matrix equation .
If we take then .
Thus eigenvector corresponding to eigenvalue is
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