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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![-1
1
-1
3.) Given the matrix A =
-2
1
1
(a) Find the singular values o; of A.
[Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X2 + 36 A.]
(b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius
norm). Note: you do NOT need to find the whole SVD to do this. Find only
those parts you need for A'.
(c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A.
Note: the matrix 2-norm is subordinate to the vector 2-norm.](https://content.bartleby.com/qna-images/question/b8d14a18-18b6-4b9f-91b0-8c8acc9b34e2/ad4fde69-9a59-4c82-a013-189376960d6c/i64dg3_thumbnail.png)
Transcribed Image Text:-1
1
-1
3.) Given the matrix A =
-2
1
1
(a) Find the singular values o; of A.
[Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X2 + 36 A.]
(b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius
norm). Note: you do NOT need to find the whole SVD to do this. Find only
those parts you need for A'.
(c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A.
Note: the matrix 2-norm is subordinate to the vector 2-norm.
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