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  • Fix vectors v1,…,vm∈Rdv_1,\dots,v_m\in\mathbb{R}^d with 1≤d≤m1\le d\le m. For integers kk satisfying 2≤k≤d2\le k\le d, let ∣vi1∧⋯∧vik∣|v_{i_1}\wedge\cdots\wedge v_{i_k}| denote the Euclidean norm of the…