In the paper by A. J. Coleman, "The greatest mathematical paper of all time" (Math Intelligencer, 11, no. 3 (1989), 29-39), on page 30 there is a passing remark that the "Jordan form is due to Weierstrass". Can anyone give a reference to Weierstrass's publications or to a history source that discusses this?
According to the following linked text, Weierstrass defined his equivalent form in a memoir presented to the Berlin Academy in 1868, two years prior to Jordan's Traite being published.
On the history of Jordan Normal Forms, see Thomas Hawkins "Weierstrass and the Theory of Matrices" Archive for History of Exact Sciences 17, p 119-163 (1977). In section four of this paper, Hawkins shows that Weierstrass, in his theory of Elementary Divisors, has already defined a normal form equivalent to that of Jordan. Weierstrass presented his fundamental memoir "Zur Theorie der bilinearen und quadratischen Formen" to the Berlin Academy in 1868 (Monatsberichte, p. 311-338 = Werke 2, p.19-44) two years before the publication of Jordan's Traite.
Another nice source relative to this controversy between Weierstrass, Kronecker and Jordan is the review "Sur les progrès de la théorie des invariants projectifs" by Franz Meyer from 1897. As the link to Google books put earlier on MathOverflow does not seem to give access to the full text anymore, another link one can use is this one. The relevant discussion is between pages 27 and 35.