Is there a definition of determinant of a non - square matrix??
What would you like that determinant "to do"?
Many of the roles played by the ordinary determinant for square matrices simply won't be inherited by your type of determinant. And what would then be the point of specifying an algorithm that would have as its output some number we call the "determinant" of that matrix?
I'm sure you could define a 'determinant like' thing for non-square matrices. Just define it however you need it and make it match intuition.
You would want to make sure that it had useful properties and obeyed regular properties of determinants. It could be quite an undertaking to come up with anything useful.
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