Below you will find example sentences with "linear operators". The examples show how this phrase is used in natural context and which words often surround it.
Linear Operators in a sentence
Corpus data
- Displayed example sentences: 19
- Discovered as a combination around: operators
- Corpus frequency in the collocation scan: 9
- Phrase length: 2 words
- Average sentence length: 23.3 words
Sentence profile
- Phrase position: 7 start, 12 middle, 0 end
- Sentence types: 19 statements, 0 questions, 0 exclamations
Corpus analysis
- The phrase "linear operators" has 2 words and usually appears in the middle in these examples. The average sentence has 23.3 words and is mostly made up of statements.
- Around this phrase, patterns and context words such as of bounded linear operators on a, based on linear operators rather than, space, algebra and operator stand out.
- In the phrase index, this combination connects with drone operators and linear shaped, linking the page to nearby combinations.
Example types with linear operators
This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:
Linear operators are ubiquitous in the theory of quantum mechanics. (10 words)
Linear operators also play a great role in the infinite-dimensional case. (12 words)
Linear operators main The most common kind of operator encountered are linear operators. (13 words)
The assignment f ↦ f ∗ produces an injective linear map between the space of linear operators from V to W and the space of linear operators from W ∗ to V ∗ ; this homomorphism is an isomorphism if and only if W is finite-dimensional. (42 words)
The elements of topological vector spaces are typically functions or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particular notion of convergence of sequences of functions. (36 words)
A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: * A is a topologically closed set in the norm topology of operators. (33 words)
Example sentences (19)
Linear operators seeAlso Linear operators acting on kets A linear operator is a map that inputs a ket and outputs a ket.
The assignment f ↦ f ∗ produces an injective linear map between the space of linear operators from V to W and the space of linear operators from W ∗ to V ∗ ; this homomorphism is an isomorphism if and only if W is finite-dimensional.
Linear operators main The most common kind of operator encountered are linear operators.
A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: * A is a topologically closed set in the norm topology of operators.
Linear operators acting on bras Operators can also be viewed as acting on bras from the right hand side.
This is why very different techniques are employed when studying linear operators (and operators in general) in the infinite-dimensional case.
An important object of study in functional analysis are the continuous linear operators defined on Banach and Hilbert spaces.
Bounded linear operators over Banach space form a Banach algebra in respect to the standard operator norm.
It was developed in parallel with a new approach to the mathematical spectral theory based on linear operators rather than the quadratic forms that were David Hilbert 's approach a generation earlier.
Linear operators also play a great role in the infinite-dimensional case.
Linear operators are ubiquitous in the theory of quantum mechanics.
Many sets of linear operators in functional analysis are endowed with topologies that are defined by specifying when a particular sequence of functions converges to the zero function.
Note that the associative property does not hold for expressions that include non-linear operators, such as the antilinear time reversal operator in physics.
Operator topologies If X and Y are topological vector spaces, the space L(X,Y) of continuous linear operators f:X Y may carry a variety of different possible topologies.
Since virtually every calculation in quantum mechanics involves vectors and linear operators, it can involve, and often does involve, bra-ket notation.
Some properties of this notation are convenient since we are dealing with linear operators and composition acts like a ring multiplication.
The elements of topological vector spaces are typically functions or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particular notion of convergence of sequences of functions.
The space B(H) of bounded linear operators on a Hilbert space H is a fundamental example of C*-algebra.
When the Banach algebra A is the algebra L(X) of bounded linear operators on a complex Banach space X (e.