Determinant of a non square matrix

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The discussion centers on the concept of defining a determinant for non-square matrices, highlighting that traditional properties of determinants for square matrices do not apply. Participants question the purpose of creating a determinant-like measure for non-square matrices, emphasizing the need for it to have useful properties. Any proposed definition should align with intuitive understanding and maintain some regular characteristics of determinants. The conversation suggests that while it is possible to create such a definition, it could be complex and challenging. Ultimately, the feasibility and utility of a determinant for non-square matrices remain uncertain.
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Is there a definition of determinant of a non - square matrix??
 
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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