My textbook indicates that the set of all upper triangular n ✕ n matrices is a real vector space, but the set of all upper triangular square matrices is not a real vector space.
Why is there a difference between the two? Shouldn't the upper triangular square matrix set also be a vector space?
I guess what they mean is that you need to precise that they must be the same size and that you can’t have a vectorial space of matrices of size p and of size n.
But that’s quite unclear.