Why is the Leibniz formula for determinants called such?

Question

My professor said that Leibniz was not even aware of the concept. The Wikipedia page says that the formula was named "in honor of Gottfried Leibniz." What gives? Did he do work that was related, and if so, what did his formula look like?

This answer says that Leibniz was, by way of Gerolamo Cardano, but the Wikipedia article linked there has nothing on the subject.

Edit: Here is a historical article that has the following quote:

The preface to this contains the first notable historical sketch of the theory, and includes references to the writings of twelve outstanding mathematicians, beginning with Cramer (1750) and ending with the author's own contemporaries, Cayley, Sylvester and Hermite. In the same year (1850) there also occurred something out of the ordinary, for the correspondence between Leibnitz and the Marquis de I'Hôpital having been published from manuscripts in the Royal Library at Hanover, the striking discovery was made that more than half-a-century before Cramer's time the fundamental idea of determinants had been clear to Leibnitz, and had been expounded with considerable fullness by him in a letter to his friend.

Oh, a history and "reason for grammar" question. This is going to get closed by a moderator as "non constructive" — CogitoErgoCogitoSum, Feb 28 '13 at 04:32
I feel like wanting to know what Leibniz's description of the determinant, i.e., a mathematical one, would be constructive, but I get the same vibe. — bright-star, Feb 28 '13 at 04:34
Oh, moderator types are making arbitrary judgments. Good call, regulating which types of information are good to promote and which are not. — CogitoErgoCogitoSum, Feb 28 '13 at 04:35
@CogitoErgoCogitoSum Qiaochu just told his opinion, as the community has a lot of power here, it still can be closed if you start a vote can't it? Even Moderators are users, why shouldn't he be allowed to tell his opinion? — Dominic Michaelis, Feb 28 '13 at 04:37
@Cogito: I have no idea why you thought this was going to get closed, or why you have such a negative attitude towards the moderators. — Zev Chonoles, Feb 28 '13 at 04:37
In any case, please move this to a meta thread, as it has gone off-topic. — Mariano Suárez-Álvarez, Feb 28 '13 at 04:38
This is on the English wikipedia as well, just a less helpful link was provided in the earlier answer; see here. Leibniz was fully aware of determinants as defined by complete expansion (== Leibniz formula), and discussed it with the Bernoullis and such. — gnometorule, Feb 28 '13 at 06:56

score 2 · Answer 1 · answered Feb 28 '13 at 04:41

2

In the german wikipedia article it says that Leibniz defined it that way. One of my Professors said, that if something is named after someone, this person normally doesn't contribute anything to it.

answered Feb 28 '13 at 04:41

Dominic Michaelis

19,935

1

That's Stigler's Law for sure ;) – bright-star Feb 28 '13 at 05:37

score 2 · Accepted Answer · answered Mar 01 '13 at 13:04

Leibniz wrote to l'Hospital in 1693 explaining a rule for elimination in systems of linear equations. This letter was published in 1850, and an English translation can be found in Smith: A Source Book in Mathematics, p. 267.

There is another small note (see pp. 5-7) by Leibniz on the same subject, probably written before 1693, which was eventually published in 1863 and which is also found in the Source Book mentioned above.

Why is the Leibniz formula for determinants called such?

2 Answers2