Unitary equivalence of normal matrices over topological spaces
Unitary equivalence of normal matrices over topological spaces
复制标题
拓扑空间上正规矩阵的酉等价
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
E. Park
中科院分区：
文献类型：
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作者：
Greg Friedman;E. Park
设A和B是具有CW复形同伦型的拓扑空间X上系数为连续复值函数的正规矩阵，并假设这两个矩阵在X的每一点上具有相同的不同特征值。利用阻塞理论建立了A和B酉等价的充分必要条件。我们还确定了界限的数量可能的酉等价类的上同调不变量的X。
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point of X. We use obstruction theory to establish a necessary and sufficient condition for A and B to be unitarily equivalent. We also determine bounds on the number of possible unitary equivalence classes in terms of cohomological invariants of X.