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SVD and Signal Processing, III
book

SVD and Signal Processing, III

by M. Moonen, B. De Moor
March 1995
Intermediate to advanced content levelIntermediate to advanced
498 pages
23h 58m
English
Elsevier Science
Content preview from SVD and Signal Processing, III
Isospectral Matrix Flows for Numerical Analysis
53
where
Ad(g). ~
is defined as
d. t~
Ad(g) . ~ = --~(ge g-1)lt=o.
By differentiating
Ad(g).~
with respect to the variable g we obtain the Lie bracket operation
ad: ~ x ~ ~
(~,,7) ---, [~,
hi. (52)
We also use the notation
ad~(~)=
[~, 7/]. Then the orbit
M(~) = {Ad(g). ~ l g e G)
(53)
is a smooth compact submanifold of the Lie algebra qS.
If G is semi-simple, then the Killing form
(~, r/): =
-tr(ad~ o adn)
(54)
defines a positive definite inner product on @.
Consider for a fixed element 7/E q5 the trace function
Cn:M(~) ~ ~ , Cn(~) = ((,77).
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Publisher Resources

ISBN: 9780444821072