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Why must $0≤c_i≤1$?
2026-04-11 16:49:04.1775926144
Why must $0≤c_i≤1$?
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If $P$ is a parallelpiped in $\mathbb{R}^n$ formed by the vectors $v_1, v_2, \ldots, v_n$ then (by definition) $$ P = \{x\in\mathbb{R}^n | x=c_1v_1+c_2v_2+\ldots+c_nv_n~\text{for some}~c_1, c_2, \ldots, c_n\in [0,1]\}. $$ Hence, if $x\in T(P)$ then there are $c_1, c_2, \ldots, c_n\in [0,1]$ such that $x=T(c_1v_1+c_2v_2+\ldots+c_nv_n)$.