QR_Inverse, matrix inversion with the usage of QR decomposition. As matrix \(A\) can be decomposed into a product of an orthogonal matrix \(Q\) and an upper triangular matrix \(R\) in the form of \(A = QR\), the matrix inversion should be \(A^{-1} = R^{-1}Q^{-1} = R^{-1}Q^T\).
\[ \begin{align}\begin{aligned}AA^{-1} = I\\A = QR\\A^{-1} = R^{-1}Q^T\end{aligned}\end{align} \]
As matrix \(R\) is an upper triangular matrix, \(R^{-1}\) is easy to compute. In this design, \(R^{-1}\) is computed via Backward Substitution.