A formula for the euclidean distance between a point and a linear subspace is presented. As a consequence a formula for determinants of positive semidefinite, hermitian matrices is derived, and a formula for the loss value of multilinear regression.

中文翻译：

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多元线性回归的损失值

给出了点与线性子空间之间的欧式距离公式。因此，推导出了半正定厄米特矩阵的行列式公式，以及多线性回归的损失值公式。