Bendixson's inequality
In mathematics, Bendixson's inequality is a quantitative result in the field of matrices derived by Ivar Bendixson in 1902. The inequality puts limits on the imaginary parts of Characteristic roots of real matrices. A special case of this inequality leads to the result that characteristic roots of a real matrix are always real.
Mathematically, the inequality is stated as:
Let be a real matrix and. If is any characteristic root of, then
If is symmetric then and consequently the inequality implies that must be real.
