# Non-Square Matrix

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A Non-Square Matrix is a matrix in which the matrix horizontal length, [math]\displaystyle{ m }[/math], and matrix vertical length, [math]\displaystyle{ n }[/math] are not the same ([math]\displaystyle{ m \ne n }[/math]).

**Context:**- It can range from being a Non-Invertible Non-Square Matrix to being either a Left Invertible Non-Square Matrix (with a left inverse to being a Right-Invertible Non-Square Matrix (with a right inverse).
- It can range from being an Abstract Non-Square Matrix to being a Non-Square Matrix Structure (such as a non-square array).

**Example(s):**- a 2x3 matrix, such as [math]\displaystyle{ \begin{bmatrix}1 & 9 & 13 \\20 & 55 & 6 \end{bmatrix}. }[/math]
- a 3x2 matrix, such as [math]\displaystyle{ \begin{bmatrix} \sigma_{1} & 0 \\ 0 & \sigma_{2} \\ 0 & 0 \end{bmatrix}. }[/math]

**Counter-Example(s):****See:**Identity Matrix.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/invertible_matrix Retrieved:2015-12-5.
- … Non-square matrices (
*m*-by-*n*matrices for which m ≠ n*) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If***A**is**m**A is equal to*-by-*n and the rank of*n*, then**A**has a left inverse: an*n*-by-m*matrix**B such that***BA**= I. If**A**has rank**m**B such that*, then it has a right inverse: an*n-by-*m*matrix**AB**= I.

- … Non-square matrices (