Let A be a Hermitian matrix wih eigenvallue A, 2 , 2 · --- > an and ortho normal eigen vecloxs vector --- .. for any x in R". non zero Un. quotiend ple) o dekined by XHAX the Ray leigh くAx,×) xメ 三 くx, x>
Let A be a Hermitian matrix wih eigenvallue A, 2 , 2 · --- > an and ortho normal eigen vecloxs vector --- .. for any x in R". non zero Un. quotiend ple) o dekined by XHAX the Ray leigh くAx,×) xメ 三 くx, x>
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Question-
Let A be a Hermitian
> An
for any
madrix with eigenvalues
and ortho normal eigen vecloxs
vector x in Rn
入,と。
と
U, ,
un:
nonzero
c3 detined by.
Rayleigh quotiend ple)
the
くAx,x)
x"AX
xH x
< x, x >
15 x = C, u, +
+ Cn Un, show thad
2.
IC,lt|Cel入2t
+ICn] an
|
2.
(b)
show that
(C)
show dh at
and
mch peR)
= An
max p(x) = ,
メチ0
X +0
(4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fdbb1a7-d573-479c-8d2a-d1c6b6fb9ae3%2F2a0d64a9-0fcc-49fb-b96a-a52bd1710dd3%2Fyk5vz6e_processed.png&w=3840&q=75)
Transcribed Image Text:Question-
Let A be a Hermitian
> An
for any
madrix with eigenvalues
and ortho normal eigen vecloxs
vector x in Rn
入,と。
と
U, ,
un:
nonzero
c3 detined by.
Rayleigh quotiend ple)
the
くAx,x)
x"AX
xH x
< x, x >
15 x = C, u, +
+ Cn Un, show thad
2.
IC,lt|Cel入2t
+ICn] an
|
2.
(b)
show that
(C)
show dh at
and
mch peR)
= An
max p(x) = ,
メチ0
X +0
(4)
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