Dear All,
I'm looking for partial orders for the space of matrices .
Thanks.
Hi, for example on the space of symetric matrices, the positiveness >= 0 (all the eigenvalues of the matrix are positive) is an order relation on this space.
The positive semi-defnite condition can be used to definene a partial ordering on all symmetric matrices.
This is called the Lowner ordering or the positive semi-definite ordering. For any two symmetric
matrices A and B, we write A >= B if A - B >= 0, i.e. A-B is semi-definite
For arbitrary square matrices M, N we write M ≥ N if M - N ≥ 0; i.e., M - N is positive semi-definite. This defines a partial ordering on the set of all square matrices. One can similarly define a strict partial ordering M > N.
The wikipedia page here https://en.wikipedia.org/wiki/Positive-definite_matrix is should answer your questions.
Please look at the files I've sheared. there are some orders for matrices. Is it true?
Dear Ahmed,
In this Order we should accept that A=B if and only if det(A)=det(B). Therefore, for example:
A=[2 1, 1 2] is equal to B=[4 -1, -1 1].
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