Information about Hermitian
A number of mathematical entities are named Hermitian, after the mathematician Charles Hermite:
- Hermitian adjoint
- Hermitian form
- Hermitian function
- Hermitian matrix
- Hermitian metric
- Hermitian operator
- Hermitian transpose
- Hermitian wavelet
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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mathematician is a person whose primary area of study and research is the field of mathematics.
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Problems in mathematics
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Charles Hermite
Charles Hermite circa 1887
Born November 24 1822
Dieuze, Lorraine, France
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Charles Hermite circa 1887
Born November 24 1822
Dieuze, Lorraine, France
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adjoint operator. Adjoints of operators generalize conjugate transposes of square matrices to (possibly) infinite-dimensional situations. If one thinks of operators on a Hilbert space as "generalized complex numbers", then the adjoint of an operator plays the role of the complex
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In mathematics, a sesquilinear form on a complex vector space V is a map V × V → C that is linear in one argument and antilinear in the other.
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In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign:
for all in the domain of of .
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for all in the domain of of .
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A Hermitian matrix (or self-adjoint matrix) is a square matrix with complex entries which is equal to its own conjugate transpose — that is, the element in the ith row and jth column is equal to the complex conjugate of the element in the j
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In 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 (holomorphic) tangent space.
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In mathematics, on a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.
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conjugate transpose, Hermitian transpose, or adjoint matrix of an m-by-n matrix A with complex entries is the n-by-m matrix A* obtained from A
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Hermitian wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The Hermitian wavelet is defined as the derivative of a Gaussian:
where denotes the Hermite polynomial.
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where denotes the Hermite polynomial.
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In mathematics, an element x of a star-algebra is self-adjoint if .
A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation.
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A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation.
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