3. Consider the matrix A = 12 of Problem 1(a). Let o1, 02 be the singular values of A. (a) Find all singular value decompositions A = 0ju¡ v{ + o2u2v%. (b) Find an orthonormal eigenbasis {v1, v2} of AT A such that A" Av; = o?v; and an orthonormal eigenbasis {u1, u2} of AAT such that AA" u; = o?u;, such that A is not equal to o1u¡ vf+o2u2v%. [Hint: The condition Av; = 0;u; is not automatic!]
3. Consider the matrix A = 12 of Problem 1(a). Let o1, 02 be the singular values of A. (a) Find all singular value decompositions A = 0ju¡ v{ + o2u2v%. (b) Find an orthonormal eigenbasis {v1, v2} of AT A such that A" Av; = o?v; and an orthonormal eigenbasis {u1, u2} of AAT such that AA" u; = o?u;, such that A is not equal to o1u¡ vf+o2u2v%. [Hint: The condition Av; = 0;u; is not automatic!]
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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3. Consider the matrix A = of Problem 1(a). Let o1, 02 be the singular values of A. (a) Find all singular value decompositions A = oju¡v} +o2u2v%. (b) Find an orthonormal eigenbasis {vị, v2} of AT A such that AT Av; = and an orthonormal eigenbasis {u1, u2} of AAT such that AA"u; = o?u;, such that A is not equal to o1u̟ vf +o2u2V½. [Hint: The condition Av; = 0;u; is not automatic!]
![3. Consider the matrix A =
of Problem 1(a). Let o1, 02 be the singular values of A.
(a) Find all singular value decompositions A =
(b) Find an orthonormal eigenbasis {v1, v2} of AT A such that
AT Av; = o?v;
and an orthonormal eigenbasis {u1, u2} of AAT such that
AA" u; = o?u,,
such that A is not equal to o¡u¡ vf+o2u2v½. [Hint: The condition Av; = 0;u; is not automatic!]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5a270a0-9262-4075-b679-b7882deb4430%2F00b40a1d-437d-475e-a0d3-f9afbcf93d74%2Fyydouzi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the matrix A =
of Problem 1(a). Let o1, 02 be the singular values of A.
(a) Find all singular value decompositions A =
(b) Find an orthonormal eigenbasis {v1, v2} of AT A such that
AT Av; = o?v;
and an orthonormal eigenbasis {u1, u2} of AAT such that
AA" u; = o?u,,
such that A is not equal to o¡u¡ vf+o2u2v½. [Hint: The condition Av; = 0;u; is not automatic!]
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