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After you've done that, please explain in one sentence with fewer than 20 words how a determinant is a measure of fullness-of-span in n-dimensional space. I kn
by shanusmagnus 11y ago
After you've done that, please explain in one sentence with fewer than 20 words how a determinant is a measure of fullness-of-span in n-dimensional space. I know that it is, but I've never understood the intuition.
- teraflop 11y agoA determinant describes changes in volume under transformation, and an (n-1)-dimensional set of points has zero n-dimensional volume. (very sketchy, but it's the best I could come up with under the constraints)
- shanusmagnus 11y agoBrilliant effort!
- bcoates 11y agoV. I. Arnold uses 17 words: "The determinant of a matrix is an (oriented) volume of the parallelepiped whose edges are its columns." http://pauli.uni-muenster.de/~munsteg/arnold.html http://pauli.uni-muenster.de/~munsteg/arnold.html