Search results
Results from the WOW.Com Content Network
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 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.
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 ...
By the Gershgorin circle theorem, all of the eigenvalues of a stochastic matrix have absolute values less than or equal to one. Additionally, every right stochastic matrix has an "obvious" column eigenvector associated to the eigenvalue 1: the vector 1 used above, whose coordinates are all equal to 1.
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 ...
For example, ) is a hollow matrix. Properties ... The Gershgorin circle theorem shows that the moduli of the eigenvalues of a hollow matrix are less or equal to the ...
Below are some examples. Rump's example In the 1980s, Rump made an example. ... Kantorovich theorem; Gershgorin circle theorem; Ulrich W. Kulisch; References Further ...
Five circles theorem – Derives a pentagram from five chained circles centered on a common sixth circle; 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 ...