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

1. ## how 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?

2. ## Re: how do you prove determinant expand by the Leibniz formula or the Laplace formula

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 $\displaystyle K:\mathbb{R}^n\times\cdots\times\mathbb{R}^n\to \mathbb{R}$ for which $\displaystyle \det(I)=1$? If so, see my blog post here. If not, give us the definition you're using.

3. ## Re: 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.

5. ## Re: how do you prove determinant expand by the Leibniz formula or the Laplace formula

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