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Denoting or relating to a matrix in which those pairs of elements which are symmetrically placed with respect to the principal diagonal are complex conjugates.
‘In general, the eigenvalues can be complex numbers, even when the elements of the matrix are real, but the symmetry of a Hermitian matrix ensures that all the eigenvalues will be real.’
‘Finally he speculates on the future, and the hope of finding at last a Hermitian operator whose resonances describe the zeros of the zeta function.’
‘It was 1942 before he was able to defend his doctoral thesis on Hermitian operator theory and the generalised moment problem.’
‘Do you realize that's the pair-correlation function for the eigenvalues of a random Hermitian matrix?’
‘Hermite is now best known for a number of mathematical entities that bear his name: Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices.’
Origin
Early 20th century: from the name of Charles Hermite (1822–1905), French mathematician, + -ian.