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Approximations with real linear modules. (English) Zbl 1140.65034

The author further develops the real linear approximation theory by regarding \( \mathbb{C} ^{n}\) as a module over the ring of circlets. He proposes improved approximations upon the standard complex Hilbert space techniques, using a new concept of orthogonality together with the respective Gram-Schmidt ortogonalization process. Related hierarchical bases are devised leading to a new family of rapidly constructible family of unitary matrices. Complex matrix approximation is also considered through finding the nearest real matrix in small rank perturbations.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A04 Linear transformations, semilinear transformations
65F25 Orthogonalization in numerical linear algebra
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References:

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