Square Matrix

A matrix for which horizontal and vertical dimensions are the same (i.e., an n×n matrix).

A matrix m may be tested to determine if it is square in Wolfram Language using SquareMatrixQ[m].

Consider the numbers of n×n matrices on n^2 distinct symbols. The number of distinct matrices modulo rotations and reflections for n=1, 2, ... are given by 1, 3, 45360, ... (OEIS A086829).

Consider an n×n matrix consisting of the integers 1 to n^2 arranged in any order. Then the maximal determinants possible for n=1, 2, ... are 1, 10, 412, 40800, 6839492, ... (OEIS A085000).

Consider an n×n matrix with single copies of the digits 1, 2, ..., d and the rest of the elements zero. Then the triangle of n×n matrices with digits d=0, 1, ..., n^2 that are rotationally and reflectively distinct is 1, 1; 1, 1, 2, 3, 3; 1, 3, 12, 66, 378, 1890, 7560, 22680, 45360, 45360; ... (OEIS A087074).

See also

Array, Magic Square, Matrix, Rectangular Matrix, Square Array

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Sloane, N. J. A. Sequences A085000, A087074, and A086829 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Square Matrix

Cite this as:

Weisstein, Eric W. "Square Matrix." From MathWorld--A Wolfram Web Resource.

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