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Rank on symbolic matrices

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Ohad Shapira
Ohad Shapira on 4 Apr 2021
Edited: Bruno Luong on 7 Apr 2021
Hey all,
I'm trying to figure out the rank of several (sym) matrices that I am working on and the built-in 'Rank' function gives me different answer.
As I saw in the help, It's not reliable and I can't trust it ("rank returns an incorrect result because the outputs of intermediate steps are not simplified").
Is there a different way to get the rank of my matrices?
Bruno Luong
Bruno Luong on 5 Apr 2021
According to it seems you cannot use RANK until a numerical value is plugged-in.
Seem like very limited usefulness to me.
That reminds me why I don't like using computer symbolic calculation.
Ohad Shapira
Ohad Shapira on 5 Apr 2021
Thanks, most of my problems are solved in this forum.
BTW, your scenario:

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Answers (1)

Aditya Patil
Aditya Patil on 7 Apr 2021
Rank does not take identities satisfied by functions into account. As a workaround, substitute values into variables, and then calculate rank. See Rank Function Does Not Simplify Symbolic Calculations more further details.
Ohad Shapira
Ohad Shapira on 7 Apr 2021
Thank you,
I saw this and I'm trying to understand what can I do to "fix" the rank function that it will return the right answer.
What can I do to verify it?
Bruno Luong
Bruno Luong on 7 Apr 2021
Edited: Bruno Luong on 7 Apr 2021
May be you can select p arbitrary combinations of values of your variables and substitute in then calculation of the rank after substitution.
If the ranks obtained after substitution give the identical result then it is ikely this holds true for almost all values.
I would suggest select p as the size of the matrix (n) + 1 or larger, because the determinant is a polynomial of order n, threfore has n+1 DOFs.

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