Search results
Results from the WOW.Com Content Network
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 discs coincide with the spectrum, the matrix is diagonal.
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 ...
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
I suspect the theorem is also in Franklin's "Matrix Theory" and, perhaps, Golub and Van Loan. Quarteroni et al refer to Atkinson "An Intro to Num. Anal" pp 588 for the proofs. So, if some wants to write it up, I think it definitely belongs on the main page -- I don't have time currently to write it up myself. Lavaka 15:18, 16 November 2007 (UTC)
Pages for logged out editors learn more. Contributions; Talk; Gerschgorin circle theorem
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.
Bill Clinton “Hillary and I mourn the passing of President Jimmy Carter and give thanks for his long, good life,” Clinton, the country's 42nd president, said in a statement on Sunday.