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.
References
Spectral abscissa Wikipedia(Text) CC BY-SA