Real logarithms of semi-simple matrices. (English) Zbl 1526.15007
Summary: We study the differential and topological structures of the set of real logarithms of any semi-simple non-singular matrix and of the set of real skew-symmetric logarithms of any special orthogonal matrix.
MSC:
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 22E30 | Analysis on real and complex Lie groups |
| 53C30 | Differential geometry of homogeneous manifolds |
| 15B10 | Orthogonal matrices |
Keywords:
logarithm matrix; semi-simple matrix; orthogonal matrix; skew-symmetric matrix; unitary matrix; homogeneous space; homotopy sequence of a bundle; generalized principal real logarithmSoftware:
mftoolboxReferences:
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