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