The geometric mean decomposition. (English) Zbl 1063.15009
Let \({\mathbb C}\) be the field of complex numbers. The matrix \({\mathbb H}\) in \({\mathbb C}^{m\times m}\) is said to have a geometric mean decomposition if \({\mathbb H}\)=QRP\(^\star\), where \({\mathbb P}\), \({\mathbb Q}\) are matrices with orthonormal columns and \({\mathbb R}\) is a real upper triangular matrix with diagonal elements all equal to the geometric mean of the positive singular values of \({\mathbb H}\).
The authors develop algorithms for computing the geometric mean decomposition of a matrix \({\mathbb H}\). The interest in this problem arose in signal processing.
The authors develop algorithms for computing the geometric mean decomposition of a matrix \({\mathbb H}\). The interest in this problem arose in signal processing.
Reviewer: Erich W. Ellers (Toronto)
MSC:
15A23 | Factorization of matrices |
65F25 | Orthogonalization in numerical linear algebra |
94A11 | Application of orthogonal and other special functions |
60G35 | Signal detection and filtering (aspects of stochastic processes) |
94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
geometric mean decomposition; matrix factorization; unitary factorization; singular value decomposition; Schur decomposition; QR decomposition; MIMO systems; algorithms; signal processingReferences:
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