Let $\mathbf{z}_1,\mathbf{z}_2,\cdots,\mathbf{z}_{n-1},\mathbf{y}$ represent orthogonal basis for $\mathbb{R}^n$. Then how to prove the following \begin{equation} \sum\limits_{i=1}^{n-1}\alpha_i\mathbf{y}^T\mathbf{z}_i = 0 \end{equation} where, $\alpha_i\in\mathbb{R}$
2026-04-08 20:23:00.1775679780
prove the following about orthogonal basis in n dimension
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