how do you prove determinant expand by the Leibniz formula or the Laplace formula is the same?

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- Jul 15th 2011, 09:20 AMvictorluihow do you prove determinant expand by the Leibniz formula or the Laplace formula ...
how do you prove determinant expand by the Leibniz formula or the Laplace formula is the same?

- Jul 15th 2011, 10:44 AMDrexel28Re: how do you prove determinant expand by the Leibniz formula or the Laplace formula
It depends what your definition of the determinant is. Do you define it as the unique alternating multilinear form $\displaystyle K:\mathbb{R}^n\times\cdots\times\mathbb{R}^n\to \mathbb{R}$ for which $\displaystyle \det(I)=1$? If so, see my blog post here. If not, give us the definition you're using.

- Jul 15th 2011, 10:48 AMChandler26Re: how do you prove determinant expand by the Leibniz formula or the Laplace formula
Hello,

It sounds more difficult as it really is.

You know the determinant is a multilinear map and the definition of the adjugate matrix. - Jul 15th 2011, 11:26 AMvictorluiRe: how do you prove determinant expand by the Leibniz formula or the Laplace formula
my definition of determinant is in here:

Leibniz formula for determinants - Wikipedia, the free encyclopedia - Jul 15th 2011, 01:30 PMDrexel28Re: how do you prove determinant expand by the Leibniz formula or the Laplace formula