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# Square Matrix

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

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

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

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

Consider an matrix with single copies of the digits 1, 2, ..., and the rest of the elements zero. Then the triangle of matrices with digits , 1, ..., 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

## References

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

Square Matrix

## Cite this as:

Weisstein, Eric W. "Square Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SquareMatrix.html