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)
“The variables of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)