Determinant of a non square matrix

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SUMMARY

The discussion centers on the concept of defining a determinant for non-square matrices. It establishes that traditional properties of determinants for square matrices do not apply to non-square matrices, raising questions about the utility of such a definition. Participants suggest that while a "determinant-like" concept can be created for non-square matrices, it must be carefully defined to ensure it possesses useful properties and aligns with intuitive expectations. The conversation emphasizes the complexity involved in developing a meaningful determinant for non-square matrices.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly determinants.
  • Familiarity with matrix theory and properties of square matrices.
  • Knowledge of mathematical intuition regarding matrix operations.
  • Experience with defining mathematical constructs and their properties.
NEXT STEPS
  • Research the properties of determinants in linear algebra.
  • Explore alternative definitions of determinants for non-square matrices.
  • Investigate applications of non-square matrices in various mathematical contexts.
  • Study the implications of determinant-like constructs in computational mathematics.
USEFUL FOR

Mathematicians, students of linear algebra, and researchers interested in matrix theory and its applications will benefit from this discussion.

praharmitra
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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.
 

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