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Was V.I. Arnold wrong when he said everything a student needs to know about determinants is derived from geometric considerations? It seems true to me that, out
by woopsn 2y ago
Was V.I. Arnold wrong when he said everything a student needs to know about determinants is derived from geometric considerations? It seems true to me that, outside of advanced study linear or abstract algebra, this is the one perspective which can at least dispel the magic.
- Syzygies 2y agoYes, in real space the determinant is the signed volume of the image of the unit cube. Volume is base x height. Height is a linear function in the vector that rises above the base; the usual properties of the determinant follow from this.