Bounds for departure from normality and the Frobenius norm of matrix eigenvalues
New lower and upper bounds for the departure from normality and the Frobenius norm of the eigenvalues of a matrix axe given. The significant properties of these bounds axe also described. For example, the upper bound for matrix eigenvalues improves upon the one derived by Kress, de Vries and Wegmann in [Lin. Alg. Appl., 8 (1974), pp. 109-120]. The upper bound for departure from normality is sharp for any matrix whose eigenvalues are collinear in the complex plane. Moreover, the latter formula is a practical estimate that costs (at most) 2m multiplications, where m is the number of nonzeros in the matrix. In terms of applications, the results can be used to bound from above the sensitivity of eigenvalues to matrix perturbations or bound from below the condition number of the eigenbasis of a matrix.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 10114083
- Report Number(s):
- ORNL/TM-12853; ON: DE95006144
- Resource Relation:
- Other Information: PBD: Dec 1994
- Country of Publication:
- United States
- Language:
- English
Similar Records
The use of strain tensor to estimate thoracic tumors deformation
Bounds for Departure from Normality and the Frobenius Norm of Matrix Eigenvalues