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The cofactor expansion is a special case of a more generalised expansion rule (see page 10 of Harley
Flanders' Differential Forms book). I came here looking for it before I recalled I had a good reference. If no one objects I'll try adding a section about this.
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I added a simple example of how the complementary minor expansion works, unfortunately you need to be looking at at least the 4 by 4 case for it to be different from the usual cofactor expansion.
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Laplace expansion mentioned here. As a physicist I have not heard of Laplace's 'formula' before, so I am curious as to common usages and what is deemed correct. --
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Why does "Laplace's
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Maybe nice to mention that especially with matrices with many 0-valued cells this technique makes it very easy to calculate the determinant? --
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Laplace expansion of a determinant by complementary minors
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https://en.wikipedia.org/Leibniz_formula_for_determinants
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The proof is easier to understand if the reader consults
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