Talk:Determinant (mathematics)

[edit] "Unique number"?

What does "a determinant is a unique number" (my emphasis) mean? Does that imply that the relationship between a determinant and its matrix is one-to-one, or, in other words, that every determinant is unique in that it has only one matrix associated with it? Because, in my understanding of mathematics, that is not the case. It might be a good idea to clarify that phrase: perhaps "special number" is closer to what is intended?

Disclaimer: I am not a mathematician. ;-) —Thomas Larsen (talk) 16:40, 7 January 2011 (EST)

I am not a mathematician either. Yet, I'm surprised that the phrase "a unique number associated with a matrix" is open to confusion. I let the sentence stand, but formalized it straightaway by introducing a map from the matrix to a number. A map (function) has a unique image and hence it associates the matrix with a unique number. I removed "namely in linear algebra", because determinants appear in other branches of mathematics, too. I wanted to indicate that the determinant appears most often in linear algebra, but if that is not clear, it is better not to say anything about it. The reader is supposed to know what a matrix is, anyway, and then knows about linear algebra. The specification mathematics is necessary because I believe that biology (evolution theory) also uses the term.--Paul Wormer 04:19, 8 January 2011 (EST)

Okay, fair enough; thanks for the clarification. I like the way you've redone the introduction.—Thomas Larsen (talk) 05:11, 8 January 2011 (EST)