Question

How many elementsare there in a triangular sparse matrix?

Answer 1

Well, I guess you simply want the number of triangular matrix entries in an N×NN×Nmatrix. . So without the diagonal it is N(N−1)/2N(N−1)/2 and including the diagonal it is N(N+1)/2N(N+1)/2.

Using your notation, matrix indices are usually indexed starting with 1, so you get the results via

∑n=1N∑m=n+1N1=N(N−1)/2∑n=1N∑m=n+1N1=N(N−1)/2

and

∑n=1N∑m=nN1=N(N+1)/2