Square Matrix

AKA: n×n Matrix.
Context:
- It can be related to invertible matrix P and Diagonal Matrix D such that Square Matrix A [math]\displaystyle{ = P^{-1}DP }[/math].
- It can range from being a Square Binary Matrix to being a Square Integer Matrix to being a Square Real-Number Matrix to being a Complex Square Matrix.
- It can range from being a Non-Symmetric Square Matrix to being a Symmetric Square Matrix (such as a Persymmetric Matrix when it has symmetry about its Matrix Cross-Diagonal).
Example(s):
- [math]\displaystyle{ A = \begin{bmatrix} 1 & \infty \\0 & \pi \end{bmatrix} }[/math].
- any Identity Matrix.
- any Confusion Matrix.
- any Triangular Matrix.
- …
Counter-Example(s):
- a Non-Square Matrix, such as [math]\displaystyle{ A = \begin{bmatrix} 2 & 1 & 3\\1 & 2 & 3 \end{bmatrix} }[/math].
- a Vector, such as [math]\displaystyle{ A = \begin{bmatrix} 2.0 & 3.5 & 4.25\end{bmatrix} }[/math].
See: Invertible Matrix, Non-Singular Matrix.

References

(Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Matrix_%28mathematics%29#Square_matrices
- A square matrix is a matrix which has the same number of rows and columns. A n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied. A square matrix A is called invertible or non-singular if there exists a matrix B such that
  - AB = I'n.
(Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Invertible_matrix
- QUOTE: A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that if you pick a random square matrix, it will almost surely not be singular.

(WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=square%20matrix
- S: (n) square matrix (a matrix with the same number of rows and columns)