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The functions below ([`squareroot`](@ref), [`logarithm`](@ref) and [`power`](@ref) with fractional powers) are only defined for matrices whose eigenvalues avoid (part of) the negative real axis, and their principal values are complex whenever eigenvalues on that axis are present.
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In MatrixAlgebraKit, we aim to keep type stability, and thus the scalar type of the output always matches that of the input.
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As such, a real matrix with eigenvalues on the negative real axis leads to a `DomainError`, you should pass a complex matrix instead to obtain the complex principal value.
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As such, a real matrix with eigenvalues on the negative real axis leads to a `DomainError`.
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You should pass a complex matrix instead to obtain the complex principal value.
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To avoid spurious errors for eigenvalues that lie on the negative real axis only because of rounding errors (e.g. a positive semidefinite matrix with a tiny negative eigenvalue), eigenvalues within an absolute tolerance `domain_atol` of the domain boundary are clamped onto it.
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This tolerance defaults to [`default_domain_atol`](@ref) and can be specified explicitly for the algorithms that support it, e.g. `MatrixFunctionViaEigh(eigh_alg; domain_atol=...)`.
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