square matrix (thing) by ariels

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:

Wronskian	Matrix	doubly stochastic matrix	Cramer's Rule
positive semidefinite	Gaussian elimination	Determinant	negative semidefinite
Schur's Theorem	symmetric matrix	Row	symmetric
permanent	singular	Compute Fibonacci numbers FAST!	permutation matrix
Null space	Linear Independence	magic square	eigenvector
Transpose	adjoint	Rank