Numerical range

In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex formula_1 matrix "A" is the set
where formula_3 denotes the conjugate transpose of the vector formula_4.
In engineering, numerical ranges are used as a rough estimate of eigenvalues of "A". Recently, generalizations of the numerical range are used to study quantum computing.
A related concept is the numerical radius, which is the largest absolute value of the numbers in the numerical range, i.e.