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The eigenvalues of A must also lie within the Gershgorin discs C j corresponding to the columns of A. Proof. Apply the Theorem to A T while recognizing that the eigenvalues of the transpose are the same as those of the original matrix. Example. For a diagonal matrix, the Gershgorin discs coincide with the spectrum. Conversely, if the Gershgorin ...
The following results can be proved trivially from Gershgorin's circle theorem. 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.
English: Gershgorin disk theorem example. This diagram shows the discs in yellow derived for the eigenvalues. The first two disks overlap and their union contains two eigenvalues. The third and fourth disks are disjoint from the others and contain one eigenvalue each.
Gauss circle problem – How many integer lattice points there are in a circle; Gershgorin circle theorem – Bound on eigenvalues; Geometrography – Study of geometrical constructions; Goat grazing problem – Recreational mathematics planar boundary and area problem; Hadamard three-circle theorem
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.
Anderson's theorem (real analysis) Andreotti–Frankel theorem (algebraic geometry) Angle bisector theorem (Euclidean geometry) Ankeny–Artin–Chowla theorem (number theory) Anne's theorem ; Apéry's theorem (number theory) Apollonius's theorem (plane geometry) Appell–Humbert theorem (complex manifold) Arakelyan's theorem (complex analysis)
I found basically the equivalents in two books: Anne Greenbaum's "Iterative Methods for Solving Systems" as well as Quarteroni, Sacco and Saleri's "Numerical Mathematics", who provide a "Third Gershgorin Thm" as well, which holds for irreducible matrices. I suspect the theorem is also in Franklin's "Matrix Theory" and, perhaps, Golub and Van Loan.
Pages for logged out editors learn more. Contributions; Talk; Gerschgorin circle theorem