There's a geometric interpretation of the determinant of an operator in a real vector space that I've always found intuitive. Suppose we have a n-dimensional real-valued vector space. We can plot n vectors in an n-dimensional Cartesian coordinate system, and in general we'll have an n-dimensional parallelepiped. If we apply an operator to these n vectors, the result is a new parallelepiped whose "n-dimensional volume" is equal to the volume of the original parallelepiped time the (absolute value of the) determinant of the operator.(adsbygoogle = window.adsbygoogle || []).push({});

Is there an extension of this interpretation for an operator in a complex vector space?

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# Interpretation of the determinant of an operator in complex vector space

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