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- W2088939415 abstract "Let A∈Mn(C). Let σ(A) denote the spectrum of A, and F(A) the field of values of A. It is shown that if σ(A)∩(−∞,0]=∅, then A has a unique square root B∈Mn(C) with σ(B) in the open right (complex) half plane. This result and Lyapunov's theorem are then applied to prove that if F(A)∩(−∞,0]=∅, then A has a unique square root with positive definite Hermitian part. We will also answer affirmatively an open question about the existence of a real square root B∈Mn(R) for A∈Mn(R) with F(A)∩(−∞,0]=∅, where the field of values of B is in the open right half plane." @default.
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- W2088939415 date "2001-01-01" @default.
- W2088939415 modified "2023-10-18" @default.
- W2088939415 title "Uniqueness of matrix square roots and an application" @default.
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- W2088939415 doi "https://doi.org/10.1016/s0024-3795(00)00243-3" @default.
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