What does the following quote by Sylvester mean?

"A general algebraical determinant in its developed form may be likened to a mixture of liquids seemingly homogeneous, but which, being of differing boiling points, admit of being separated by the process of fractional distillation."

I find it hard to come up with mathematical analogies to reasonably explain the quote (found in Artin's Algebra.)

  • $\begingroup$ I suppose some chemistry knowledge would help you $\endgroup$ Jul 17, 2023 at 11:10
  • $\begingroup$ Is it possible that he is referring to Laplace's recursive method where a determinant is expressed as a linear combination of the determinants of sub-matrices. $\endgroup$
    – nwr
    Jul 17, 2023 at 18:46
  • $\begingroup$ Ah, that seems reasonable. @nwr $\endgroup$ Jul 17, 2023 at 19:17
  • 3
    $\begingroup$ Outside my area of expertise, thus a comment. The meaning of the quoted text should become clearer by referring to the original publication: J. J. Sylvester, "Note on Determinants and Duadic Disynthemes." American Journal of Mathematics, Vol. 2, No. 1, Mar. 1879, pp. 89-96 (scan online) $\endgroup$
    – njuffa
    Jul 17, 2023 at 21:19


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