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Let \(A \in \mathbb{K}^{m \times n}\), where \(\mathbb{K}\) is \(\mathbb{R}\) or \(\mathbb{C}\). The Moore-Penrose psuedoinverse of $A$ is the unique $n \times m$ matrix $A^+$ such that:

If \(A\) is full rank \(R=\min(m, n)\), then:

- If \(A\) has linearly independent columns == \(A^* A\) is invertible, then

is a *left* inverse of \(A\) i.e. \(A^+ A = I_{n \times n}\)

- If \(A\) has linearly independent rows == \(A A^*\) is invertible, then

is a *right* inverse of \(A\) i.e. \(A A^+ = I_{m \times m}\)