QR and LQ Decomposition Matrix Backpropagation Algorithms for Square, Wide, and Deep -- Real or Complex -- Matrices and Their Software Implementation

Denisa A. O. Roberts, Lucas R. Roberts

This article presents matrix backpropagation algorithms for the QR decomposition of matrices $A_{m,n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k…