Square Matrix (original) (raw)
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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
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References
Sloane, N. J. A. Sequences A085000, A087074, and A086829 in "The On-Line Encyclopedia of Integer Sequences."
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Square Matrix." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SquareMatrix.html