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The MP inverse exists and is unique for any matrix \(A\). When \(A\) has linearly independent columns, the MP inverse \(A^+\) is \[ A^+ = (A^* A)^{-1 } A^* \]

Where \(A^*\) is the conjugate transpose of \(A\).

If the rows are linearly independent, \[ A^+ = A^* (AA^*)^{-1} \].