Unitary divisor
In mathematics, a natural number ''a'' is a unitary divisor (or Hall divisor) of a number ''b'' if ''a'' is a divisor of ''b'' and if ''a'' and \frac are coprime, having no common factor other than 1. Equivalently, a divisor ''a'' of ''b'' is a un ...
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Unitary element In mathematics, an element of a *-algebra is called unitary if it is invertible and its inverse element is the same as its adjoint element.
Definition
Let \mathcal be a *-algebra with unit An element a \in \mathcal is called unitary if In o ...
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Unitary group
Unitary may refer to:
Mathematics
* Unitary divisor
* Unitary element
* Unitary group
* Unitary matrix
* Unitary morphism
* Unitary operator
* Unitary transformation
* Unitary representation
* Unitarity (physics)
* ''E''-unitary inverse semi ...
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Unitary matrix
In linear algebra, an invertible complex square matrix is unitary if its matrix inverse equals its conjugate transpose , that is, if
U^* U = UU^* = I,
where is the identity matrix.
In physics, especially in quantum mechanics, the conjugate ...
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Unitary morphism
In category theory, a branch of mathematics, a dagger category (also called involutive category or category with involution) is a category equipped with a certain structure called ''dagger'' or ''involution''. The name dagger category was coined b ...
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Unitary operator
In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product.
Non-trivial examples include rotations, reflections, and the Fourier operator.
Unitary operators generalize unitar ...
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Unitary transformation
In mathematics, a unitary transformation is a linear isomorphism that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
Formal definition
More precise ...
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Unitary representation
In mathematics, a unitary representation of a group ''G'' is a linear representation π of ''G'' on a complex Hilbert space ''V'' such that π(''g'') is a unitary operator for every ''g'' ∈ ''G''. The general theory is well-developed in the ca ...
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Unitarity (physics)
In quantum physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom ...
Unitary authority
A unitary authority is a type of local government, local authority in New Zealand and the United Kingdom. Unitary authorities are responsible for all local government functions within its area or performing additional functions that elsewhere are ...
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Unitary state
A unitary state is a (Sovereign state, sovereign) State (polity), state governed as a single entity in which the central government is the supreme authority. The central government may create or abolish administrative divisions (sub-national or ...
See also
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Unital (disambiguation) Unital may refer to:
* A unital algebra – an algebra that contains a multiplicative identity element.
* A geometric unital – a block design for integer .
* A unital algebraic structure
In mathematics, an algebraic structure or algebraic sy ...
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Unitarianism
Unitarianism () is a Nontrinitarianism, nontrinitarian sect of Christianity. Unitarian Christians affirm the wikt:unitary, unitary God in Christianity, nature of God as the singular and unique Creator deity, creator of the universe, believe that ...