Rank on symbolic matrices

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?

TIA

[Steven Lord]

What would you want MATLAB to return for the rank of this matrix?

X = sym('x', [2, 2])

X = 

No, I'm not going to tell you anything about the elements inside X.

[Ohad Shapira]

It will be of rank of 2,

In my scenario I have the matrix:

A=sym([sin(w*t)^2-1, cos(w*t);
            cos(w*t)^2, cos(w*t)])
rank(A)

Output= 2

But as you can see, the elements in the first culomn are equal (trigonometric identities) so I would expect to get rank=1

[Bruno Luong]

"But as you can see, the elements in the first culomn are equal (trigonometric identities) so I would expect to get rank=1"

I'm only aware that sin(w*t)^2-1 is equal to MINUS cos(w*t)^2

[Ohad Shapira]

@Bruno Luong You got me there, still, same results:

[Bruno Luong]

When a is used? When t is declared as real?

[Ohad Shapira]

I tested t as real, gets the same result.

Originally 'a' was a coefficient of the trigonometrials, to simplify it I removed it's use.

[Bruno Luong]

Maybe some one that own symbolic tbx can help you (I don't) but I wonder what do you get with an even simpler matrix

A=sym([t, w*t; 1, w]);
rank(A)

[Bruno Luong]

According to https://www.mathworks.com/help/symbolic/rank.html 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]

Thanks, most of my problems are solved in this forum.

BTW, your scenario:

Answer 1

[Aditya Patil]

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]

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]

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.