Spectral abscissa
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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
Matrices[]
Let λ1, ..., λs be the (real or complex) eigenvalues of a matrix A ∈ Cn × n. Then its spectral abscissa is defined as:
For example, if the set of eigenvalues were = {1+3i,2+3i,4-2i}, then the Spectral abscissa in this case would be 4.
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.
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Categories:
- Spectral theory
- Matrix theory
- Linear algebra stubs