Answered: 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

Section: Chapter Questions

Problem 1RQ

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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/

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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