Batas Perturbasi Mutlak Nilai Eigen dari Matriks Normal

Dewi Ika Ainurrofiqoh; Merysa Puspita Sari; Sailah Ar Rizka; Nadia Kholifia

doi:10.37905/euler.v13i2.31084

Batas Perturbasi Mutlak Nilai Eigen dari Matriks Normal

Dewi Ika Ainurrofiqoh, Merysa Puspita Sari, Sailah Ar Rizka, Nadia Kholifia

Abstract

The eigenvalue problem in matrices is an important topic in numerical computation, particularly in analyzing the sensitivity of eigenvalues to disturbances or perturbations. This study discusses the absolute perturbation bounds on the eigenvalues of a matrix, focusing on normal matrices and their relationship to the condition of normal matrices. Based on existing theorems, the absolute perturbation bounds are presented in various forms involving the Frobenius norm and the condition number of the matrix eigenvectors. This research provides a detailed discussion of results concerning the absolute perturbation bounds on eigenvalues and their applications to normal matrices. Ultimately, an important result on the error bounds of eigenvalues in the case of normal matrices affected by perturbations is fully explained, proving the connection between the absolute error bound and the Frobenius norm of the perturbations.

Keywords

Eigenvalues; Perturbation Bounds; Normal Matrices; Frobenius Norm; Eigenvalue Error

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DOI: https://doi.org/10.37905/euler.v13i2.31084

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