Bauer–Fike theorem

The set of Bauer- Fike (after Friedrich Ludwig Bauer and CT Fike, 1960) is a set of numerical mathematics. It provides an estimate of the variation of the eigenvalues ​​of a matrix on the basis of interference.

Be a submultiplikative matrix norm, a diagonalizable matrix with eigenvalues ​​and one fault. Then each eigenvalue in the spectrum of at most has the following distance to the spectrum of:

With the condition number and a matrix having the eigenvectors as a column, i.e..