How I can separate a matrix that is not positive definite, into two matrices?

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hossen hassanzadth 2021 年 3 月 31 日
I want to separate a matrix that is not positive definite, into two matrices in Matlab like this:
for example this matrix:

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回答 (1 件)

John D'Errico 2021 年 3 月 31 日

Are you asking to find a new matrix Sq, such that the linear algebraic product Sq'*sq is equal to Q, where Q is NOT positive definite? NO. That is impossible.
Are you asking to find two matrices S and q, such that the product of the 4 matrices S*q'*S*q is Q? (I highly doubt this is your question, but you explicitly said TWO matrices.)
Since the first is impossible, you asking to find some matrix Sq such that Sq' * Sq is as close as possible to Q, based on some norm on the difference?
Are your matrices real, or are they complex? Must the solution live in the real domain?
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hossen hassanzadth 2021 年 4 月 1 日
hi
I want to find Sq, such that the linear algebraic product Sq'*Sq is equal or as close as possible to Q.
solution can be in real or complex domain.

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