what is the geometric meaning of the determinant?

Asked Oct 29 '23 at 21:46

Active Oct 29 '23 at 21:46

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I have come across a few definitions that describe the geometric meaning of the (absolute value) determinant, such as:

How is it that the determinant can mean both of those things?

asked Oct 29 '23 at 21:46

Kuskuba

Think about what the matrix does to the unit $n$-cube ... (e.g. if $n=2$ then I mean the square with vertices at $(0,0), (1,0), (0,1), (1,1)$). – Noah Schweber Oct 29 '23 at 21:51
4

Does this answer your question? What's an intuitive way to think about the determinant? – blargoner Oct 29 '23 at 21:52
Voting to close as a duplicate; to address "how [can] the determinant mean both of those things?", the volume "defined by the columns of a square matrix" is the volume of the image of the unit cube, which is equal to the scale factor for volume of a linear transformation multiplied by the volume of the unit cube. – Andrew D. Hwang Oct 29 '23 at 23:40

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