For A∈ℂ^(n x m), the Moore-Penrose inverse A^(+)∈ℂ^(m x n) is a matrix, satisfying all of the following conditions:

${\text{1.}}\quad AA^{+}A$ $=\;A$

${\text{2.}}\quad A^{+}AA^{+}$ $=\;A^{+}$

${\text{3.}}\quad (AA^{+})^{*}$ $=\;AA^{+}$

${\text{4.}}\quad (A^{+}A)^{*}$ $=\;A^{+}A$

The Moore-Penrose inverse exists for any A and is unique.