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While I basically understand what a determinant is, I wonder how this idea was developed? What was the principal idea behind its origination? I would like to know this so that I can have a better conceptualization of the determinant.

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    +1 good question. You're in for a wilder ride than you probably thought. Determinants were arguably the first linear algebra concept to be invented -- before abstract vector spaces, before even matrices. There were just these strange expressions that kept popping up when quite different problems were solved the hard way. Sometime along the way someone noticed that they were all structured similarly and gave them a name. I hope you get some good historical references in answers.2011-11-13
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    Non-duplicate: [where did determinant come from?](http://math.stackexchange.com/questions/62732/) which was closed as a duplicate of a _non-historical_ intuition-of-determinants question. One of the answers before it was closed links to an interesting historical wall-of-text, though.2011-11-13
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    If you are looking for something involving the history of determinants (and matrices) you might start here: http://www-history.mcs.st-and.ac.uk/history/HistTopics/Matrices_and_determinants.html#862011-11-13
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    I know of two very interesting things; A chinese mathematician (B.C.) recorded the determinant of a 3x3 system; see http://books.google.co.uk/books/about/Basic_linear_algebra.html?id=40HnLsET7OEC and also Euler or Lagrange in a litter wrote down a system of equations in a letter as 11 + 12 + ... +17 = x (say) then 21 + 22 + ... + 27 = y and ... and ...81 + 82 + ... + 87 = z where 11 does not represent 11 but the first sum of the first equation - in matrix notation, if the system was represented by a matrix A cont.2012-01-25
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    11 would be writte a_1,1 and in general ij is a_ij. He wrote down a condition like 11.22.33 + ... - 12.34.25 = 0 for the system to have a solution that's non-trivial, that is the determinant.2012-01-25

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