Landweber exact functor theorem

In mathematics, the spectral abscissa of a matrix or a bounded linear operator is the supremum among the real part of the elements in its spectrum, sometimes denoted as $\eta (A)$

Matrices

Let λ₁, ..., λ_s be the (real or complex) eigenvalues of a matrix A ∈ C^{n × n}. Then its spectral abscissa is defined as:

$\eta (A)={\max }_i\{\mathrm{R}\mathrm{e}({\lambda }_i)\}$

It is often used as a measure of stability in control theory, where a continuous system is stable if all its eigenvalues are located in the left half plane, i.e. $\eta (A)<0$

See also

Spectral radius

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