
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Let {u1, u2, . . . , un} be an orthonormal basis for Rn
and let A be a linear combination of the rank 1
matrices u1uT1
, u2uT2
, . . . , unuTn
. If
A = c1u1uT1
+ c2u2uT2
+· · ·+cnunuTn
show that A is a
c1, c2, . . . , cn and that ui is an eigenvector
belonging to ci for each i.
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