论文标题
有限顺序矩阵的同时块对角线
Simultaneous Block Diagonalization of Matrices of Finite Order
论文作者
论文摘要
众所周知，仅当矩阵通勤时，只有一组非缺陷矩阵可以对角度化。在非公认矩阵的情况下，可以实现的最好的是同时进行对角线化。在这里，我们给出了一种有效的算法，以明确计算转移矩阵，该矩阵实现了单位矩阵的同时块对角线化，其分解在不可减至的块中（常见不变子空间）是从其他地方知道的。我们的主要动机在于粒子物理学，其中必须明确地知道所产生的转移矩阵，以便明确确定外部自多态性的作用，例如平等，电荷共轭或时间逆转在粒子光谱上。
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we give an efficient algorithm to explicitly compute a transfer matrix which realizes the simultaneous block diagonalization of unitary matrices whose decomposition in irreducible blocks (common invariant subspaces) is known from elsewhere. Our main motivation lies in particle physics, where the resulting transfer matrix must be known explicitly in order to unequivocally determine the action of outer automorphisms such as parity, charge conjugation, or time reversal on the particle spectrum.
