algebra

does (A inverse ) exist for non square matrix?
In general matrix inverses are not defined for non-square matrices. However one can define left or right inverses depending on the matrix. For example the column matrix C
C=(0.50.5)\displaystyle C\, =\, \begin{pmatrix}0.5\\0.5\end{pmatrix}
has the left inverse row matrix R
R=(1.01.0)\displaystyle R\, =\, \begin{pmatrix}1.0&1.0\end{pmatrix}
since
R C = 1
In this particular case there can be no right inverse. For more details, see
https://en.wikipedia.org/wiki/Invertible_matrix
for example
 
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