Let U be an m x m matrix, let V be ann x n matrix, and let where E, is an n xn diagonal matrix with diagonal entries o1, 02,...,0o, and O is the (m – n) x n zero matrix. (a) Show that ifU = (U1, U2), where U, has n columns, then UΣ-U (b) Show that if A = UEV", then A can be ex- pressed as an outer product expansion of the form A = oju, v +0zuzv +...+ G,U,v

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 U be an m x m matrix, let V be ann x n matrix,
and let
where E, is an n xn diagonal matrix with diagonal
entries o1, 02,...,0o, and O is the (m – n) x n zero
matrix.
(a) Show that ifU = (U1, U2), where U, has n
columns, then
UΣ-U
(b) Show that if A = UEV", then A can be ex-
pressed as an outer product expansion of the
form
A = oju, v +0zuzv +...+ G,U,v
Transcribed Image Text:Let U be an m x m matrix, let V be ann x n matrix, and let where E, is an n xn diagonal matrix with diagonal entries o1, 02,...,0o, and O is the (m – n) x n zero matrix. (a) Show that ifU = (U1, U2), where U, has n columns, then UΣ-U (b) Show that if A = UEV", then A can be ex- pressed as an outer product expansion of the form A = oju, v +0zuzv +...+ G,U,v
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