Hermitian
Encyclopedia
A number of mathematical entities are named Hermitian, after the mathematician
Charles Hermite
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Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Charles Hermite
Charles Hermite
Charles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
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- Hermitian adjointHermitian adjointIn mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator.Adjoints of operators generalize conjugate transposes of square matrices to infinite-dimensional situations...
- Hermitian connectionHermitian connectionIn mathematics, the Hermitian connection \nabla, also called the Chern connection, is the unique connection on a Hermitian manifold that satisfies the following conditions,# It preserves the metric g, i.e., \nabla g=0....
, the unique connection on a Hermitian manifold that satisfies specific conditions - Hermitian form, a specific sesquilinear form
- Hermitian function, a complex function whose complex conjugate is equal to the original function with the variable changed in sign
- Hermitian hat waveletHermitian hat waveletThe Hermitian hat wavelet is a low-oscillation, complex-valued wavelet.The real and imaginary parts of this wavelet are defined to be thesecond and first derivatives of a Gaussian respectively:...
, a low-oscillation, complex-valued wavelet
- Hermitian manifoldHermitian manifoldIn mathematics, a Hermitian manifold is the complex analog of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each tangent space...
/structure- Hermitian metric, is a smoothly varying positive-definite Hermitian form on each fiber of a complex vector bundle
- Hermitian matrix, a square matrix with complex entries that is equal to its own conjugate transpose
- Hermitian operator, bounded symmetric operators
- Hermitian polynomials, a classical orthogonal polynomial sequence that arise in probability
- Hermitian symmetric spaceHermitian symmetric spaceIn mathematics, a Hermitian symmetric space is a Kähler manifold M which, as a Riemannian manifold, is a Riemannian symmetric space. Equivalently, M is a Riemannian symmetric space with a parallel complex structure with respect to which the Riemannian metric is Hermitian...
, a Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space - Hermitian transposeConjugate transposeIn mathematics, the conjugate transpose, Hermitian transpose, Hermitian conjugate, or adjoint matrix of an m-by-n matrix A with complex entries is the n-by-m matrix A* obtained from A by taking the transpose and then taking the complex conjugate of each entry...
, the transpose of a matrix and with the complex conjugate of each entry - Hermitian varietyHermitian varietyHermitian varieties are in a sense a generalisation of quadrics, and occur naturally in the theory of polarities.-Definition:Let K be a field with an involutive automorphism \theta...
, a generalisation of quadrics - Hermitian wavelet, a family of continuous wavelets