Normal approximations of commuting square-summable matrix families
Linear Algebra and its Applications, ISSN: 0024-3795, Vol: 703, Page: 11-19
2024
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Article Description
For any square-summable commuting family (Ai)i∈I of complex n×n matrices there is a normal commuting family (Bi)i no farther from it, in squared normalized ℓ2 distance, than the diameter of the numerical range of ∑iAi⁎Ai. Specializing in one direction (limiting case of the inequality for finite I ) this recovers a result of M. Fraas: if ∑i=1ℓAi⁎Ai is a multiple of the identity for commuting Ai∈Mn(C) then the Ai are normal; specializing in another (singleton I ) retrieves the well-known fact that close-to-isometric matrices are close to isometries.
Bibliographic Details
Elsevier BV
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