A matrix with as many rows as it has columns; an "n×n" matrix.

Dignifying "square" matrices with their own name may seem silly, even downvotable. But, seen as linear transformations, square matrices preserve dimension -- thus they map a vector space to itself.

Accordingly, many concepts make sense only for squares, or are simpler there. For example, all these involve square matrices, only:

• Determinants
• Permanents
• permutation matrices
• A graph's adjacency matrix
• More generally, any transition matrix
• Multi-dimensional second derivatives: the Wronskian