Determine the dimension of each of the

-vector spaces of matrices with real coefficients and order n x n:

- the space of all these matrices --->I know that the dimension of this one is n

^{2} , the number of elements

CORRECT
- the space of diagonal matrices ---> would this be n?

YES
- the space of the upper triangular matrices ----->I would say this is n

^{2}/2 + n/2 (half of the matrix plus the other half diagonal), but I'm not sure

- the space of the symmetric matrices

- the space of the antisymmetric matrices.