De nombreuses sources affirment qu'il l'aurait fait en 1848, mais Sylvester n'a rien publié cette année-là. (voir The Collected Mathematical Papers of James Joseph Sylvester (Cambridge, England: Cambridge University Press, 1904), vol. 1.). Sa première utilisation du terme matrix, en 1850, figure dans Additions to the articles in the September number of this journal, “On a new class of theorems,” and on Pascal's theorem, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 37 : 363-370. (1850), page 369 : « For this purpose we must commence, not with a square, but with an oblong arrangement of terms consisting, suppose, of m lines and n columns. This will not in itself represent a determinant, but is, as it were, a Matrix out of which we may form various systems of determinants […] ».
« I have in previous papers defined a “Matrix” as a rectangular array of terms, out of which different systems of determinants may be engendered as from the womb of a common parent » dans The Collected Mathematical Papers of James Joseph Sylvester : 1837–1853, Article 37, p. 247.
Voir par exemple : (en) Henri Bourlès et Bogdan Marinescu, Linear Time-Varying Systems : Algebraic-Analytic Approach, Springer, , 638 p. (ISBN978-3-642-19726-0 et 3-642-19726-4, lire en ligne), §§ 2.2.4-2.2.6 ; cette formulation est très courante dans la théorie des D-modules.
(de) Karl Weierstrass, Collected works, vol. 3, (lire en ligne), p. 271–286
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(en) Alfred Tarski, Introduction to Logic and the Methodology of Deductive Sciences, Dover Publications, Inc, New York NY, 1946 (ISBN0-486-28462-X). (lire en ligne)