For a subspace S of ${\mathbb{C}}^n$ and a fixed basis, we study the compact and convex set $\begin{array}{rl}{m}_S& =\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{x}\mathrm{h}\mathrm{u}\mathrm{l}\mathrm{l}\{|s{|}^2\in {\mathbb{R}}_{\ge 0}^n:s\in S\mathrm{a}\mathrm{n}\mathrm{d}\Vert s\Vert =1\}\\ & \simeq \left\{\mathrm{Diag}\right(Y)\in M_n^h(\mathbb{C}):Y\ge 0,\mathrm{t}\mathrm{r}(Y)=1,P_{S}Y{P}_S=Y\}\end{array}$that we call the moment of S, where $|s{|}^2=(|s_1{|}^2,|s_2{|}^2,\dots ,|s_n{|}^2)$. This set is relevant in the determination of minimal hermitian matrices ($M\in M_n^h$ such that $\Vert M+D\Vert \le D$ for every diagonal D and the spectral norm $\Vert \cdot \Vert$). We describe extremal points and certain curves of $m_S$ in terms of principal vectors that minimize the angle between S and the coordinate axes of the fixed basis. We also relate $m_S$ to the joint numerical range W of n rank one $n\times n$ hermitian matrices constructed with orthogonal projection $P_S$ and the fixed basis $\{e_i{\}}_{i=1}^n$ used. This connection provides a new approach to the description of $m_S$ and to minimal matrices. As a consequence, the intersection of two of these joint numerical ranges corresponding to orthogonal subspaces allows the construction or detection of a minimal matrix.

对于一个子空间S${\mathbb{C}}^n$和一个固定的基础，我们研究紧集和凸集$\begin{array}{rl}{米}_{\mathrm{小号}}& =\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{电子}\mathrm{X}\mathrm{H}\mathrm{你}\mathrm{升}\mathrm{升}\{|秒{|}^{\mathrm{2个}}\in {\mathbb{R}}_{\ge 0}^n:秒\in \mathrm{小号}\mathrm{A}\mathrm{n}\mathrm{d}\Vert 秒\Vert =\mathrm{1个}\}\\ & \simeq \left\{\mathrm{诊断}\right(是)\in {米}_n^H(\mathbb{C}):是\ge 0,\mathrm{吨}\mathrm{r}(是)=\mathrm{1个},P_{\mathrm{小号}}是P_{\mathrm{小号}}=是\}\end{array}$我们称之为S的时刻，其中$|秒{|}^{\mathrm{2个}}=(|{秒}_{\mathrm{1个}}{|}^{\mathrm{2个}},|{秒}_{\mathrm{2个}}{|}^{\mathrm{2个}},\dots \dots ,|{秒}_n{|}^{\mathrm{2个}})$. 该集合与最小厄尔米特矩阵的确定有关（$米\in {米}_n^H$这样$\Vert 米+丁\Vert \le 丁$对于每个对角线D和谱范数$\Vert \cdot \Vert$). 我们描述极值点和某些曲线${米}_{\mathrm{小号}}$根据最小化S和固定基的坐标轴之间的角度的主向量。我们也涉及${米}_{\mathrm{小号}}$到n阶一的联合数值范围W$n\times n$用正交投影构造的厄米矩阵$P_{\mathrm{小号}}$和固定基础$\{{\mathrm{电子}}_{我}{\}}_{我=\mathrm{1个}}^n$用过的。这种联系提供了一种新的方法来描述${米}_{\mathrm{小号}}$和最小矩阵。因此，这些对应于正交子空间的联合数值范围中的两个的交集允许构造或检测最小矩阵。