A book that shows history of mathematics and how ideas were formed?
Prime 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).
T But Macduffee Vectors and Matrices (1942) and Gantmacher Matrix Theory (1953, trans 1959) both use ATAT. Macduffee's 1933 The Theory of Matrices has some relevant info: on page 5, when the term transpose and his symbol ATAT first appear, he gives a footnote reading
Or conjugate. Many different notations for the transpose have been used, as A′A′, A¯A¯, A˘A˘, A∗A∗, A1A1, tAtA. The present notation is in keeping with a systematic notation which, it is hoped, may find favor.
This makes me think Macduffee introduced the ATAT notation, and that the A′A′ notation predates it.
Neither The local library has Bocher, Introduction to Higher Algebra (1907) which does not have a special symbol for transpose.
shareciteimprove this answeredited Dec 28 '17 at 13:28answered Dec 27 '17 at 21:16📷kimchi lover8,1102925 It's worth noting that jeff560.tripod.com/matrices.html also cites Macduffee for ATAT and Wedderburn for A′A′. – Clarinetist Dec 28 '17 at 16:04 @Clarinetist Good! The site you cite is awesome! I can believe ATAT was invented by Macduffee, but surely A′A′predates Wedderburn. – kimchi lover Dec 28 '17 at 16:27 I posted an answer. I think it's the best I'll be able to find. – Clarinetist Dec 28 '17 at 16:28add a comment
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