We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the extension of the problem to $N > 2$ matrices. We compare matrix midrange statistics with the scalar and vector midrange problem and note the special significance of the matrix problem from a computational standpoint. We also study various aspects of geometric matrix midrange statistics from the viewpoint of linear algebra, differential geometry and convex optimization.

中文翻译：

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几何矩阵中频

我们为正定 Hermitian 矩阵定义几何矩阵中频，并从多个角度研究中频问题。在考虑将问题扩展到 $N > 2$ 矩阵之前，特别注意两个正定矩阵的中间范围。我们将矩阵中程统计与标量和向量中程问题进行比较，并从计算的角度注意到矩阵问题的特殊意义。我们还从线性代数、微分几何和凸优化的角度研究几何矩阵中程统计的各个方面。