A history of vector analysis
the evolution of the idea of a vectorial system
by Michael J. Crowe · first published 1967
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…matrices, which might be helpful if you want to write fast numerical code on current computers, which have been optimized to do matrix math. If you’re interested in the history, I recommend Crowe’s 1967 [History of Vector Analysis][hva]. I believe you can find the collected mathematical papers of Clifford online if you do a google search, or buy a used copy of a nice version published by Chelsea in the 1960s; the recent AMS reprint…
on “Clifford Algebra: A visual introduction (2014)” ↗For those interested in the history, I highly recommend Crowe’s book A History of Vector Analysis. It’s written a bit from the perspective of the dominant “modern” system of vectors from Gibbs/Heaviside, so it probably somewhat undersells the significance/usefulness of both Hamilton’s quaternions…
on “A Unified Mathematical Language for Physics and Engineering (1996) [pdf]” ↗There's also a great book "A History of Vector Analysis: The Evolution of the Idea of a Vectorial System" by Crowe which covers vectors from Complex numbers to Gibbs vectors and includes Hamilton and the competitor at the time Grassman Algebra, both the basis…
on “Let's remove quaternions from every 3D engine (2018)” ↗I recommend this a lot "A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)" by Michael Crowe. It's a page turner.
on “A Map of Mathematics” ↗…Spaces/Matrices/etc. become intelligible and we can begin to look at Physical problems naturally in terms of vectors/vector calculus. The following are helpful here; 1) About Vectors by Banesh Hoffmann. 2) A History of Vector Analysis: The Evolution of the Idea of a Vectorial System by Michael Crowe.
on “An illustrated introduction to linear algebra” ↗…be ranked as one of the retarders of quaternion progress, in virtue of his pamphlet on Vector Analysis, a sort of hermaphrodite monster, compounded of the notations of Hamilton and of Grassman" See "History of Vector Analysis" by Crowe or "Hamilton, Rodrigues, and the Quaternion Scandal" by Altmann. Nice to see the author cites these! The Geometric Algebra comes from Clifford Algebras, which where an attempt to combine Hamilton's…
on “Let's remove quaternions from every 3D engine (2018)” ↗…offshoot from quaternions, and has never been of the slightest use to any creature.” — William Thompson, 1st Baron Kelvin (better known as Lord Kelvin) Letter to G. F. FitzGerald (1896) as quoted in A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1994) by Michael J. Crowe, p. 120
on “A scalar triple product identity” ↗