For questions about vector spaces and their properties. More general questions about linear algebra belong under the [tag:linear-algebra] tag. A vector space is a space which consists of elements called "vectors", which can be added and multiplied by scalars. In other words, these are the spaces ...

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Positivity of the alternating sum associated to at most five subspaces

Let $V_1 , V_2 , \dots , V_n $ be proper subspaces of $ \mathbb{C}^m$ and let $$\alpha = \sum_{r=1}^n (-1)^{r+1} \sum_{ \ i_1 < i_2 < \cdots < i_r } dim(V_{i_1} \cap \cdots \cap V_{i_r})$$ ...