System and method for computing QR matrix decomposition and inverse matrix R−1. A circuit is configured to implement a QR decomposition of a matrix A into two matrices Q and R using a Modified Gram Schmidt (MGS) process. The circuit includes a specified portion dedicated to computing matrix Q. Matrix Q is computed via the specified portion based on first inputs using the MGS process, where the first inputs include the matrix A and possibly a scaling factor σ. The identity matrix may be scaled by the scaling factor σ, thereby generating scaled identity matrix σI. Scaled matrix σR−1 (or unscaled R−1) may be computed via the specified portion based on second inputs provided to the portion using the MGS process, where the second inputs include the (possibly scaled) identity matrix. If scaled, the scaled matrix σR−1 may be unscaled, thereby computing matrix R−1. Matrix R−1 is stored and/or output.