Examples of 'linear operator' in a sentence
Meaning of "linear operator"
In mathematics, a linear operator is a function or transformation that preserves the operations of addition and scalar multiplication. It is used to describe a mapping or relationship between vector spaces where the linearity property holds, meaning that the transformation behaves consistently with respect to the operations of the vector space
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- An operator L such that for functions f and g and scalar λ, L (f + g) = L f + L g and L λf = λ L f.
How to use "linear operator" in a sentence
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linear operator
We can see that is a linear operator because.
A linear operator on a metrizable vector space is bounded if and only if it is continuous.
Equivalence of continuity and boundedness of a linear operator.
In normed spaces a linear operator is continuous if and only if it is bounded.
Note that the average is a linear operator.
It also defines a linear operator on the space of all smooth functions.
Where tr denotes the trace of a linear operator.
A continuous linear operator maps bounded sets into bounded sets.
And the first is to show that it is a linear operator.
Then is a linear operator.
A linear operator is a function which satisfies the conditions of additivity and homogeneity.
On polynomial solutions of linear operator equations.
Derivative is a linear operator which inputs a function and outputs a second function.
Some properties for a linear operator.
One may study this linear operator in the context of functional analysis.
See also
Spectral decomposition of a linear operator.
Compact linear operator.
Such criterion gives a sufficient condition to a continuous linear operator be hypercyclic.
J is a linear operator.
A linear system is a mathematical model of a system based on the use of a linear operator.
Consider the linear operator.
Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
It is easy to verify that is a linear operator and that it satisfies.
The Laplace operator is an example of an unbounded positive linear operator.
Continuous linear operator.
And we showed that the Laplace transform is a linear operator.
Rank of a linear operator.
Properties of the characteristic polynomial of a finite rank real linear operator are studied.
S is a linear operator.
The Laplace transform is a linear operator.
Where is a bounded linear operator defined on a Banach space and.
So the Fourier transform is a linear operator.
An isometric surjective linear operator on a Hilbert space is called a unitary operator.
This article will discuss the case where T is a bounded linear operator on some Banach space.
Rather, a bounded linear operator is a locally bounded function.
In particular, consider the linear operator.
Any linear operator defined on a finite-dimensional normed space is bounded.
The density matrix is a representation of a linear operator called the density operator.
Every linear operator on a finite-dimensional space is trivially locally finite.
Thus a unitary operator is a bounded linear operator which is both an isometry and a coisometry.
If its domain and codomain are the same, it will then be a continuous linear operator.
It extends continuously to a bounded linear operator on H with the same operator norm.
Thus, for every physical quantity in quantum mechanics, there is a definite corresponding linear operator.
Consider the linear operator Δu uxx.
Sturm-Liouville theory concerns the action of the linear operator.
Let a be a closed linear operator densely defined on a banach space x and f em l1.
If is linear, it can be called a linear operator on.
Consider a continuous linear operator for linear operators, continuity is equivalent to being a bounded operator.
Between finite dimensional normed spaces, every linear operator is bounded.
These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis.
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