论文标题
正交相似性在对称矩阵和正交$*$上的稳定器
The stabilizers for the action of orthogonal similarity on symmetric matrices and orthogonal $*$-conjugacy on Hermitian matrices
论文作者
论文摘要
我们描述了递归算法程序，以计算相似性对所有对称矩阵集合的作用，计算复杂正交矩阵的稳定器。 futhermore，稳定器的尺寸的下限是正交$*$ - 在Hermitian矩阵上的作用。我们还证明了一个结果，可以完成正交$*$ - 共轭下的遗传矩阵正常形式的分类。我们证明的关键步骤是解决具有Toeplitz块的特定块矩阵方程。然后，将这些结果应用于在复杂的歧管中的真实codimension $ 2 $ submanifold中平面复合点的正常形式的定理。
We describe the recursive algorithmic procedure to compute the stabilizers of the group of complex orthogonal matrices with respect to the action of similarity on the set of all symmetric matrices. Futhermore, lower bounds for dimensions of the stabilizers for the action of orthogonal $*$-conjugation on Hermitian matrices are obtained. We also prove a result that completes the classification of normal forms of Hermitian matrices under orthogonal $*$-conjugation. A key step in our proof is to solve a certain block matrix equation with Toeplitz blocks. These results are then applied to provide a theorem on normal forms of the quadratic parts of flat complex points in a real codimension $2$ submanifold in a complex manifold.
