The diagonal elements of a Hermitian matrix are real.
The complex conjugate of a Hermitian matrix is a Hermitian matrix.
If is a Hermitian matrix, and is a complex matrix of same order as , then is a Hermitian matrix.
A matrix is symmetric if and only if it is real and Hermitian.
Hermitian, or self-adjoint operators on a Hilbert space play a fundamental role in quantum theories as their eigenvalues are observable, or measurable; such Hermitian operators can be represented by Hermitian matrices.
- 1 H. Eves, Elementary Matrix Theory, Dover publications, 1980.
- 2 The MacTutor History of Mathematics archive, http://www-gap.dcs.st-and.ac.uk/ history/Mathematicians/Hermite.htmlCharles Hermite
|Date of creation||2013-03-22 12:12:00|
|Last modified on||2013-03-22 12:12:00|
|Last modified by||matte (1858)|