arXiv:2610.28690v1 Announce Type: new Abstract: The F distribution arises naturally in linear regression or analysis of variance. Elementary textbooks state the result in terms of the standard normal random vector and fixed projection matrices. More advanced textbooks and research articles have extended the result to spherically symmetric random vectors. We complement the literature with a dual result that the F distribution arises with a fixed vector and random projection matrices generated by a left-spherical random matrix.