Find the dimensions of the following

A)The space of n x n matrices all of whose elements are 0 except possibly the diagonal elements.
B)The space of n x n upper triangular matrices
C))The space of n x n symmetric matrices
D)The space of n x n diagonal matrices

1 answer

A) The space of n x n matrices all of whose elements are 0 except possibly the diagonal elements has dimensions n.

B) The space of n x n upper triangular matrices has dimensions (n * (n + 1)) / 2.

C) The space of n x n symmetric matrices has dimensions (n * (n + 1)) / 2.

D) The space of n x n diagonal matrices has dimensions n.