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

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The relationship of deteminant of a matrix and its diagonol block matrix?

I am trying to prove an inequality that : $$ \operatorname{det} \Sigma_{V \mathrm{~V}}<\prod i \operatorname{det}\left(\Sigma_{V_{i} V_{i}}\right) $$ Where $$ \Sigma_{V V}=\left[\begin{array}{ccc} \Si …
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