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I have an aggregated understanding of the history of linear algebra compiled from friends, teachers, and coworkers. It may have several errors. It goes something like this:

  • Even ancient cultures like the Chinese used the idea of row reduction to solve systems of linear equations, even if the format looked somewhat different.
  • In medieval times, Arabic cultures kept this idea alive.
  • In the 18th century, European mathematicians developed matrix notation to represent a linear system. There was even now the idea of inverting that matrix.
  • By the mid 19th century, matrices were fully understood as derivatives of multivariable functions, and hence understood as transformations between finite dimensional vector spaces.

Still at this point there was limited applicability for practical problem solving. If a matrix was even moderately large, it was a nice theoretical tool, but practically impossible to compute with. So the most recent chapter is

  • In the 1940s and 1950s, with the advent of modern computing technology these limitations were overcome, and for example, Leontiff could solve a system of 500 equations.

I suppose my first question is: is any part of this significantly inaccurate? But my main question is: is anyone aware of a good historical reference emphasizing the last chapter, where computers sparked renewed interest in linear algebra? I can't seem to find any good histories that focus on this era. Most of what I find focuses on the theory developed up to the mid 19th century.

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See math.ucdavis.edu/~daddel/linear_algebra_appl/History/… for some references. –  lhf Feb 4 '12 at 19:15
    
Yes, I found these after some Googling too. But they do not emphasize the era of computing. –  alex.jordan Feb 4 '12 at 19:28
    
I don't remember ever having seen an article that collectively discusses the history of numerical linear algebra; I do know this set of talks, and these oral histories: Dongarra, Duff, Golub, Moler, Lawson, and Wilkinson, which are of interest. –  J. M. Feb 9 '12 at 7:49
    
You might also want to look into this book it deals with the history of numerics in general, but you should be able to glean out the parts dealing with linear algebra. –  J. M. Feb 9 '12 at 7:59
    
Thanks everyone for the references! –  alex.jordan Feb 9 '12 at 17:37
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You might find this article helpful, and there are additional references given: http://igitur-archive.library.uu.nl/math/2001-0227-150344/eighistory.pdf The article concentrates on issues about eigenvalues but also deals more generally with numerical linear algebra.

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