I can not seem to find any derivation or reasoning for the co-factor expansion formula we use for nxn matrices in linear algebra for determinants. Can someone please explain where we get this expansion formula from or what the logic behind it is. Thank you.
2026-04-06 22:36:34.1775514994
What is the logic and intuition behind co-factor expansion?
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There are many different approaches to determinants, and I don't know which definition you've seen. But it's fairly straightforward to derive it from the Leibniz formula $$\det(A) = \sum_{\sigma\in S_n} \text{sgn}(\sigma) \prod_{i=1}^n a_{i,\sigma(i)}$$ See e.g. Wikipedia.