eigenvalues of a Hermitian matrix are real
The eigenvalues of a Hermitian (or self-adjoint) matrix are real.
Proof.
Suppose is an eigenvalue of the self-adjoint matrix with non-zero eigenvector . Then .
Since is non-zero by assumption, is non-zero as well and so , meaning that is real. ∎
Title | eigenvalues of a Hermitian matrix are real |
---|---|
Canonical name | EigenvaluesOfAHermitianMatrixAreReal |
Date of creation | 2013-03-22 14:23:09 |
Last modified on | 2013-03-22 14:23:09 |
Owner | Andrea Ambrosio (7332) |
Last modified by | Andrea Ambrosio (7332) |
Numerical id | 8 |
Author | Andrea Ambrosio (7332) |
Entry type | Theorem |
Classification | msc 15A57 |