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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

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Naive generalization of determinant from matrices to higher rank tensors

Recall that using the Levi-Cevita symbol the determinant can be written as $$\operatorname{det} A=\frac{1}{n!}\epsilon_{i_1\dots i_n}\epsilon_{j_1\dots j_n}A_{i_1j_1}\dots A_{i_nj_n}$$ Some computatio …