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-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I.