Matrix inverse

If a matrix is really just the coefficients in a system of linear equations , then its inverse is the coefficients that allow you to solve that system, .

There are algorithms for finding the exact inverse of a matrix (if it exists). In practice, though, brute-forcing the exact inverse is overkill, and we usually use the pseudo-inverse instead. This has the added benefit of providing a well-defined result even for non-invertible matrices, such as for non-square matrices and singular matrices.