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Find an SVD of the matrix 70 000 A 0 3 00 0000

Find an SVD of the matrix 70 000 A 0 3 00 0000

Advanced Engineering Mathematics
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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Q 1. Find an SVD of the matrix 7 0007 A 0 3 00 0000 Q 2. Use the SVD of A to prove that ||A| = trace (ATA). Q3. Prove that A+ A is an orthogonal projection where A+ is the pseudo-inverse of A. Q4. Use SVD of A to show that if matrix A is full row-rank then the pseudo-inverse is given by A+ = AT (AA)-¹. Verify that this happens to be the right inverse of the matrix A.
Transcribed Image Text:Q 1. Find an SVD of the matrix 7 0007 A 0 3 00 0000 Q 2. Use the SVD of A to prove that ||A| = trace (ATA). Q3. Prove that A+ A is an orthogonal projection where A+ is the pseudo-inverse of A. Q4. Use SVD of A to show that if matrix A is full row-rank then the pseudo-inverse is given by A+ = AT (AA)-¹. Verify that this happens to be the right inverse of the matrix A.
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