left half-plane
31Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …
32Matsubara frequency — In thermal quantum field theory, the Matsubara frequency summation is the summation over discrete imaginary frequency. It takes the following form , where the imaginary frequency ω is usually taken from either of the following two sets (with ) …
33Stiff equation — In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise …
34Chebyshev filter — Linear analog electronic filters Network synthesis filters Butterworth filter Chebyshev filter Elliptic (Cauer) filter Bessel filter Gaussian filter Optimum L (Legendre) filter Linkwitz Riley filter …
35Hurwitz polynomial — In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half plane of the complex plane, that is, the real part of every zero is… …
36Bézout matrix — In mathematics, a Bézout matrix (or Bézoutian) is a special square matrix associated to two polynomials. Such matrices are sometimes used to test the stability of a given polynomial.DefinitionLet f ( z ) and g ( z ) be two complex polynomials of… …
37Routh–Hurwitz theorem — In mathematics, Routh–Hurwitz theorem gives a test to determine whether a given polynomial is Hurwitz stable. It was proved in 1895 and named after Edward John Routh and Adolf Hurwitz.NotationsLet f(z) be a polynomial (with complex coefficients)… …
38Cauchy index — In mathematical analysis, the Cauchy index is an integer associated to a real rational function over an interval. By the Routh Hurwitz theorem, we have the following interpretation: the Cauchy index of : r ( x )= p ( x )/ q ( x ) over the real… …
39Angel problem — The angel problem is a question in game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite… …
40Polar decomposition — In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z where r is the absolute value of z (a… …
