History Question - QR Factorization I'm about to teach QR factorization and I would be curious to know why the orthogonal matrix is typically denoted $Q$ and the upper triangular matrix is denoted $R$
 A: Before the QR decomposition, there was the QR algorithm. 
Without searching too much, it looks like  Rutishauser (1958) had an LR algorithm, where L and R stand for "left" and "right" triangular (instead of the now common lower and upper). 
Then Francis (1961) writes "the transformation matrices used by Rutishauser are triangular. In this paper it is proved that the transformations can be unitary, and QR transformation, as I have (somewhat arbitrarily) named this modification of Rutishauser algorithm, is shown to be particularly suitable for unsymmetric matrices which are first reduced to almost triangular form". 

References


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*J.G.F. Francis, "The QR Transformation, I", The Computer Journal, 4(3), pages 265–271 (1961, received October 1959). doi:10.1093/comjnl/4.3.265

*Rutishauser, H. (1958) Solution of eigenvalue problems with the LR–transformation. Further Contributions
to the Solution of Simultaneous Linear Equations and the Determination of Eigenvalues.
Applied Mathematics Series, vol. 49. National Bureau of Standards, pp. 47–81.
