.6 Let A = [a¡] E M, have rank r 2 1 and let A = VEW* be a singular value decomposition in which £ = diag(ơ1, 02, . . . , and W = [W¡] are in M„. Show that each entry of A can be represented as aij = Ei=1 OkVikWjk- On), V = [vij], %3D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 60EQ
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.6 Let A = [a;] E M, have rank r 2 1 and let A = VEW* be a singular
value decomposition in which = diag(ơj, 02, ..., on), V = [vij],
and W = [Wi] are in M,. Show that each entry of A can be
represented as aij = Ei=1 OkVikWjk-
Transcribed Image Text:.6 Let A = [a;] E M, have rank r 2 1 and let A = VEW* be a singular value decomposition in which = diag(ơj, 02, ..., on), V = [vij], and W = [Wi] are in M,. Show that each entry of A can be represented as aij = Ei=1 OkVikWjk-
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