how do you prove determinant expand by the Leibniz formula or the Laplace formula ...

**victorlui** · July 15th 2011, 09:20 AM

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

**Drexel28** · July 15th 2011, 10:44 AM

Originally Posted by victorlui

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

It depends what your definition of the determinant is. Do you define it as the unique alternating multilinear form $K:\mathbb{R}^n\times\cdots\times\mathbb{R}^n\to \mathbb{R}$ for which $\det(I)=1$ ? If so, see my blog post here. If not, give us the definition you're using.

**Chandler26** · July 15th 2011, 10:48 AM

Hello,

It sounds more difficult as it really is.

You know the determinant is a multilinear map and the definition of the adjugate matrix.

**victorlui** · July 15th 2011, 11:26 AM

my definition of determinant is in here:
Leibniz formula for determinants - Wikipedia, the free encyclopedia

**Drexel28** · July 15th 2011, 01:30 PM

Originally Posted by victorlui

my definition of determinant is in here:
Leibniz formula for determinants - Wikipedia, the free encyclopedia

Then I have no idea what your question means. What are you actually asking?

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