For example, we have rank=2 in MATLAB and rank=1 in WolframAlpha for a matrix shown below.
- Mathematica: http://www.wolframalpha.com/input/?i=rank(%7B%7B1-sin(x)%5E2,+cos(x)%5E2%7D,+%7B1,+1%7D%7D)
- MATLAB:
>> syms x
>> A = [1-sin(x)^2 cos(x)^2; 1 1]
A =
[ 1 - sin(x)^2, cos(x)^2]
[ 1, 1]
>> rank(A)
ans =
2
This issue is related to this topic: https://www.mathworks.com/help/symbolic/rank.html?s_tid=doc_ta#bupsf9u-1
The most general and practical workaround of this issue would be to use simplify or vpa before calling rank function.
In your case, the elements of the matrix are trigonometric functions, so rewrite function might help. https://www.mathworks.com/help/symbolic/rewrite.html
>> rewrite(A,'cos')
ans =
[ cos(x)^2, cos(x)^2]
[ 1, 1]
>> rank(rewrite(A,'cos'))
ans =
1
