2 1 1 131 1 M = 1 1 1 4 1 1 1 n+1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Hi! I have a question about Linear Algebra, could you please help me to solve it?

Q: How to prove that the matrix M shown in the figure is positive definite for complex vectors?

I know that if we want to prove a matrix is positive definite, we need to show that "x_T*M*x >0" is true. But I don't know how to prove it for complex vectors. I am so confused about it. Could you please tell me how to solve it? Thank you so much!

Attached is the matrix M.

2
1 1
1.
131
1
M =
1 1 4
1
1
1 11
1
n+1/
Transcribed Image Text:2 1 1 1. 131 1 M = 1 1 4 1 1 1 11 1 n+1/
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