[AgentMatt]

Can you give some examples for algorithms which aren't obviously logically connected but use the determinant for its nice properties?

[mturmon]

Two ways to compute the determinant:

1) product of eigenvalues

2) cofactor expansion (e.g., https://textbooks.math.gatech.edu/ila/determinants-cofactors...)

The second is the one I was taught first, in the context of linear system solution, but it does not seem obvious that it would be related to the product of eigenvalues. It’s kind of a weird pile of arithmetic manipulations.