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 moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.”
—Franklin D. Roosevelt (1882–1945)
“As to spelling the very frequent word though with six letters instead of two, it is impossible to discuss it, as it is outside the range of common sanity. In comparison such a monstrosity as phlegm for flem is merely disgusting.”
—George Bernard Shaw (1856–1950)