TITLE: Why are orthogonal matrices so often denoted $Q$?
QUESTION [6 upvotes]: I apologize for the stupid question in the title. Of course, we can baptize a particular given matrix as we want but, for example, the QR-decomposition has a fixed meaning.
My humble guess is that somebody had the idea to use $O$ for orthogonal Matrices and, since this clashes with $0$, then changed to $Q$.
To state an explicit Question: What is the first appearance in the literature of the term QR decomposition?

REPLY [4 votes]: The explanation that "The letter Q is a substitute for the letter O from orthogonal " may or may not be what John Francis had in mind when he introduced The QR Transformation: A Unitary Analogue to the LR Transformation (1961), but the use of these two letters to indicate the decomposition of a matrix goes back further. Here is a reference by A.H. Clifford from 1942:

The fact that Q and R are subsequent letters in the alphabet makes this a natural combination, perhaps more natural than the O $\mapsto$ Q switch.
 Golub and Uhlig suggest that Francis’s QR algorithm may have been influenced by Rutishauser’s qd algorithm, where "q" stands for "quotient". Since this lower case q refers to a vector rather than a matrix, it does not seem a likely explanation for the choice of the letter Q.