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Jan 28, 2019 at 8:23 history edited Carlo Beenakker CC BY-SA 4.0
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Dec 23, 2017 at 10:54 comment added kjetil b halvorsen Onetime I stmbled over a text "History of determinants" from the 1920's, which consistently talks about "the matrix of a determinant".
Nov 2, 2014 at 19:11 comment added Carlo Beenakker @FedericoPoloni --- well, the title of this chapter is "Multiplication of Matrices" so this is definitely what the authors wanted to explain, but indeed, they do not differentiate between $AB$, $AB^T$, $A^TB$ and $A^TB^T$, because these matrix products all have the same determinant. So they do not insist that $AB$ is the "proper" way to multiply matrices, as we would do in a course today.
Nov 2, 2014 at 18:26 comment added Vincent Beffara Well line 2 is the product.
Nov 2, 2014 at 17:41 comment added Federico Poloni The formula reported in your picture is not $C=AB$ but $C=A^TB$, and the Italian text translates to "The product of two determinants of the same order can be expressed as a single determinant as follows.". So someone with more free time than I have could argue that this is not a matrix product, but simply a composition rule for determinants that happens to be related to it.
Nov 2, 2014 at 11:35 history edited Carlo Beenakker CC BY-SA 3.0
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Nov 2, 2014 at 11:28 history edited Carlo Beenakker CC BY-SA 3.0
added 475 characters in body
Nov 2, 2014 at 8:11 history answered Carlo Beenakker CC BY-SA 3.0