Let A be an mxn matrix with a singular value decomposition A=UZV, where U is an mxm orthogonal matrix, Σ is an mxn "diagonal" matrix with r positive entries and no negative entries, and V is an orthogonal nxn matrix. Suppose A is square and invertible. Find a singular value decomposition of A-¹. -1 If f A is square, then man and so A, U, E, and V are all nxn matrices. If A is invertible as well, then rank A= and all of the diagonal entries of Σ are Which of these matrices are invertible? Select all that apply. A. U B. E C. V D. None of these Therefore, a singular value decomposition of A1 is A-1 =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let A be an mxn matrix with a singular value decomposition A = UZVT, where U is an mxm orthogonal matrix, Σ is an mxn "diagonal" matrix with r positive entries and no negative entries,
and V is an orthogonal nxn matrix.
Suppose A is square and invertible. Find a singular value decomposition of A-¹.
If A is square, then m = n and so A, U, Σ, and V are all nxn matrices. If A is invertible as well, then rank A= and all of the diagonal entries of Σ are
Which of these matrices are invertible? Select all that apply.
A. U
B. E
C. V
D. None of these
Therefore, a singular value decomposition of A-1 is A
Transcribed Image Text:Let A be an mxn matrix with a singular value decomposition A = UZVT, where U is an mxm orthogonal matrix, Σ is an mxn "diagonal" matrix with r positive entries and no negative entries, and V is an orthogonal nxn matrix. Suppose A is square and invertible. Find a singular value decomposition of A-¹. If A is square, then m = n and so A, U, Σ, and V are all nxn matrices. If A is invertible as well, then rank A= and all of the diagonal entries of Σ are Which of these matrices are invertible? Select all that apply. A. U B. E C. V D. None of these Therefore, a singular value decomposition of A-1 is A
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