A generalization of the complex Autonne–Takagi factorization to quaternion matrices
A generalization of the complex Autonne–Takagi factorization to quaternion matrices
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DOI：
10.1080/03081087.2011.618838
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发表时间：
2012-10
影响因子：
1.1
通讯作者：
R. Horn;Fuzhen Zhang
中科院分区：
文献类型：
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作者：
R. Horn;Fuzhen Zhang
复对称矩阵A总是可以分解为A = UΣU T，其中U是复酉矩阵，Σ是一个真实的对角矩阵，其对角元素是A的奇异值。这种分解可以看作是复对称矩阵的一种特殊的奇异值分解。我们提出了一个类似的特殊奇异值分解的一类四元数矩阵，包括复杂的矩阵是对称的或厄米特。
A complex symmetric matrix A can always be factored as A = UΣU T , in which U is complex unitary and Σ is a real diagonal matrix whose diagonal entries are the singular values of A. This factorization may be thought of as a special singular value decomposition for complex symmetric matrices. We present an analogous special singular value decomposition for a class of quaternion matrices that includes complex matrices that are symmetric or Hermitian.