Examples of 'self-adjoint' in a sentence
Meaning of "self-adjoint"
Self-adjoint is a mathematical term used to describe a linear operator that is equal to its own adjoint
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- Adjoint to itself.
- Being a Hilbert space operator which is Hermitian and also whose eigenvectors span the entire Hilbert space.
How to use "self-adjoint" in a sentence
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self-adjoint
Self-adjoint and unitary elements are normal.
A projection is orthogonal if and only if it is self-adjoint.
Every self-adjoint operator is maximal symmetric.
Such an operator is said to be essentially self-adjoint.
A positive element is self-adjoint and thus normal.
Hermitian matrices are also called self-adjoint.
Any self-adjoint operator is unitarily equivalent to a multiplication operator.
Of more interest is the existence of self-adjoint extensions.
Self-adjoint bounded operators and their spectral decomposition.
Diagonalisation of compact self-adjoint operators.
The class of self-adjoint operators is especially important in mathematical physics.
Diagonalization of compact self-adjoint operators.
Self-adjoint operators are used in functional analysis and quantum mechanics.
A main location often to including the self-adjoint.
The eigenvalues of a self-adjoint operator must all be real.
See also
Any physical law which can be expressed as a variational principle describes a self-adjoint operator.
We also present the self-adjoint extension, an important tool in quantum mechanics.
The famous spectral theorem holds for self-adjoint operators.
The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another.
In quantum mechanics, momentum is defined as a self-adjoint operator on the wave function.
Operators that are equal to their adjoints are called Hermitian or self-adjoint.
Each observable is represented by a self-adjoint linear operator acting on the state space.
This defines the functional calculus for bounded functions applied to possibly unbounded self-adjoint operators.
There is also a spectral theorem for self-adjoint operators that applies in these cases.
The more interesting question in this direction is whether A has positive self-adjoint extensions.
In general, spectral theorem for self-adjoint operators may take several equivalent forms.
Elements such that x * x are called self-adjoint.
There is however a spectral theorem for self-adjoint operators that applies in many of these cases.
Self-adjoint and unitary operators.
In general, a symmetric operator could have many self-adjoint extensions or none at all.
The structure of self-adjoint operators on infinite-dimensional Hilbert spaces essentially resembles the finite-dimensional case.
We have studied three particular cases where the self-adjoint operator definition is compromised.
Let A be a self-adjoint operator in a separable Hilbert space.
In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.
Non self-adjoint operator.
The next generalization we consider is that of bounded self-adjoint operators on a Hilbert space.
The lattice of self-adjoint projections ( also known as orthogonal projections ) of a von Neumann algebra.
A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation.
The Sturm-Liouville operator is a well-known example of a formal self-adjoint operator.
Symmetric operators which are not essentially self-adjoint may still have a canonical self-adjoint extension.
Of particular importance is the existence, and sometimes explicit constructions, of self-adjoint extensions.
Observables are represented by self-adjoint operators on the Hilbert space.
The Sturm - Liouville operator is a well-known example of a formal self-adjoint operator.
The spectral theorem for compact self-adjoint linear operators in Hilbert spaces.
A self-adjoint operator A on an inner product space is positive-definite if.
The states are vectors in Hilbert space, the observables self-adjoint operators on these vectors.
In this example, a self-adjoint morphism is a symmetric relation.
It can be shown that T always has self-adjoint extensions.
The fact that the self-adjoint operators in an abelian (sub) algebra V can be written.
Her research topic was ' A boundary value problem of ordinary self-adjoint differential equations with singularities.
