On the Gelfand-naimark Decomposition of a Nonsingular Matrix
نویسنده
چکیده
Let F = C or R and A ∈ GLn(F). Let s(A) ∈ R+ be the singular values of A, λ(A) ∈ C the unordered n-tuple of eigenvalues of A, a(A) := diag R ∈ R+, where A = QR is the QR decomposition of A, u(A) := diag U ∈ C, where A = LωU is any Gelfand-Naimark decomposition. We obtain complete relations between (1) u(A) and a(A), (2) u(A) and s(A), (3) u(A) and λ(A), and (4) a(A) and λ(A). We also study the relations between any three elements among u, λ, a, s.
منابع مشابه
On Gelfand-naimark Decomposition of a Nonsingular Matrix
Let F = C or R and A ∈ GLn(F). Let s(A) ∈ R+ be the singular values of A, λ(A) ∈ C the unordered n-tuple of eigenvalues of A, a(A) := diagR ∈ R+, where A = QR is the QR decomposition of A, u(A) := diagU ∈ C, where A = LωU is any Gelfand-Naimark decomposition. We obtain complete relations between (1) u(A) and a(A), (2) u(A) and s(A), (3) u(A) and λ(A), and (4) a(A) and λ(A). We also study the re...
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