Birkhoff and MacLane, Survey of Modern Algebra (1953), Faddeeva, Computational Methods of Linear Algebra (trans 1959), and P. Halmos, Finite Dimensional Vector Spaces (1958) all use A′A′for the transpose of AA. As do Wedderburn Lectures on Matrices (1934) and Turnbull and Aitken Theory of Canonical Matrices (1932).