I consider myself to be an inexperienced Mathematica user so maybe someone could point out what am I doing wrong.
In short, here is what I want to get: suppose that there is a matrix of dimension $ N \times N $. I know that at least one of the eigenvalues should always be zero. What I need to determine is the maximum number of non-zero eigenvalues; no need for explicit ones. I found out that the function
MatrixRank should do it. I came across one of the matrices, which seemed to "violate" the rule for eigenvalues, in the sense that I wasn't getting a zero eigenvalue. Later I was pointed out that determinant of the given matrix is "0".
Here comes the issue. 2 functions return different results for a matrix of dimension 3:
Simplify[Det[M]] -> 0 MatrixRank[M] -> 3
Due to the specific matrix being way too long, I include a link to it. This is the original matrix, I use
TrigToExp afterwards as it seemed to reduce the computation process time. In both cases I got the same result for
P.S. I need a symbolic evaluation and am currently using Mathematica 18.104.22.168.