# Square Matrix

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A square matrix is a matrix where the matrix row count is equal to the matrix column count.

**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).

- It can be related to invertible matrix
**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

### 2011

- (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._{}

- A
- (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.

- QUOTE: A square matrix that is not invertible is called

### 2009

- (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)