Question

Which is the best way to store a symmetric matrix in memory?

It would be good to save half of the space without compromising speed and complexity of the structure too much. This is a language-agnostic question but if you need to make some assumptions just assume it’s a good old plain programming language like C or C++..

It seems a thing that has a sense just if there is a way to keep things simple or just when the matrix itself is really big, am I right?

Just for the sake of formality I mean that this assertion is always true for the data I want to store

matrix[x][y] == matrix[y][x]

Answer 1

I find that many high performance packages just store the whole matrix, but then only read the upper triangle or lower triangle. They might then use the additional space for storing temporary data during the computation.

However if storage is really an issue then just store the n(n+1)/2 elements making the upper triangle in a one-dimensional array. If that makes access complicated for you, just define a set of helper functions.

In C to access a matrix matA you could define a macro:

#define A(i,j, dim) ((i <= j)?matA[i*dim + j]:matA[j*dim + i])

then you can access your array nearly normally.