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In mathematics, the Gershgorin circle theorem may be used to bound the spectrum of a square matrix. It was first published by the Soviet mathematician Semyon Aronovich Gershgorin in 1931. Gershgorin's name has been transliterated in several different ways, including Geršgorin, Gerschgorin, Gershgorin, Hershhorn, and Hirschhorn.
Gershgorin's circle theorem itself has a very short proof. A strictly diagonally dominant matrix (or an irreducibly diagonally dominant matrix [2]) is non-singular. A Hermitian diagonally dominant matrix with real non-negative diagonal entries is positive semidefinite. This follows from the eigenvalues being real, and Gershgorin's circle ...
The Gershgorin circle theorem applies the companion matrix of the polynomial on a basis related to Lagrange interpolation to define discs centered at the interpolation points, each containing a root of the polynomial; see Durand–Kerner method § Root inclusion via Gerschgorin's circles for details.
Semyon Aronovich Gershgorin (August 24, 1901 – May 30, 1933) was a Soviet (born in Pruzhany, Belarus, Russian Empire) mathematician.He began as a student at the Petrograd Technological Institute in 1923, became a Professor in 1930, and was given an appointment at the Leningrad Mechanical Engineering Institute in the same year.
Geroch's splitting theorem (differential geometry) Gershgorin circle theorem (matrix theory) Gibbard–Satterthwaite theorem (voting methods) Girsanov's theorem (stochastic processes) Glaisher's theorem (number theory) Gleason's theorem (Hilbert space) Glivenko's theorem (mathematical logic) Glivenko's theorem (probability) Glivenko–Cantelli ...
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Fundamental theorem of finitely generated abelian groups; G. Gershgorin circle theorem; H. Haran's diamond theorem;
This result known as the Gershgorin circle theorem has been used as a basis for extension. In 1964 Brenner reported on Theorems of Gersgorin Type . [ 10 ] In 1967 at University of Wisconsin—Madison , working in the Mathematics Research Center, he produced a technical report New root-location theorems for partitioned matrices .