论文标题
阳性矩阵的符号特征值和痕量最小化定理
Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem
论文作者
论文摘要
通常，通过威廉姆森的对角线形式为对称正定矩阵定义了符号特征值。标准特征值（包括痕量最小化定理）的许多特性扩展到符号特征值的情况。在本说明中，我们将概括威廉姆森的对角线形式，以使对称阳性矩阵的对称正定矩阵的情况下，这使我们能够定义符号性特征值，并在新环境中证明痕量最小化定理。
Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, are extended to the case of symplectic eigenvalues. In this note, we will generalize Williamson's diagonal form for symmetric positive-definite matrices to the case of symmetric positive-semidefinite matrices, which allows us to define symplectic eigenvalues, and prove the trace minimization theorem in the new setting.
