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 Hermitian adjoint 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 values of the numbers in the numerical range, i.e.
r(A) is a norm.
Read more about Numerical Range: Properties, Generalisations, See Also
Famous quotes containing the words numerical and/or range:
“The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.”
—Ralph Waldo Emerson (1803–1882)
“Jane Addams, founder of Hull House, once asked, “How shall we respond to the dreams of youth?” It is a dazzling and elegant question, a question that demands an answer—a range of answers, really, spiraling outward in widening circles.”
—William Ayers, U.S. author. To Teach: The Journey of a Teacher, ch. 7 (1993)