Numerical range

In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex n × n matrix A is the set In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex n × n matrix A is the set where x* denotes the conjugate transpose of the vector x. In engineering, numerical ranges are used as a rough estimate of eigenvalues of A. Recently, generalizations of 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. r(A) is a norm. r(A) ≤ ||A|| ≤ 2r(A) where ||A|| is the operator norm of A.