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Determinant of linearly independent vectors

Let w_1, w_2, \dots, w_n be unitary linearly independent vectors. Evaluate the determinant

    \[\mathcal{D} = \det \left(n \mathbb{I}-\sum_{i=1}^n w_i \otimes w_i \right)\]

where w_i \otimes w_i denotes the outer product.


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