Unformatted text preview: LU factorizations of A and B . When are there no solutions? 6. Let U 1 and U 2 be two uppertriangular matrices. Let Z be an m × n matrix. Let X be an unknown matrix that satisﬁes the equation U 1 X + XU 2 = Z. A. Give an algorithm to ﬁnd X in O ( mn ( m + n )) ﬂops (ﬂoatingpoint operations). B. Find conditions on U 1 and U 2 which guarantee the existence of a unique solution X . C. Give a nontrivial example ( U 1 6 = 0, U 2 6 = 0, X 6 = 0) where those conditions are not satisﬁed and U 1 X + XU 2 = 0 ....
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 Fall '10
 Chandrashekharan
 xT Ax, class website

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