Sentences with LINEAR-OPERATOR
Check out our example sentences below to help you understand the context.Sentences
1
"In linear algebra, a linear operator is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication."
2
"A linear operator maps every linear combination of vectors to the corresponding linear combination of their images."
3
"The composition of two linear operators is also a linear operator."
4
"A linear operator can be represented by a matrix in certain cases."
5
"The sum of two linear operators is also a linear operator."
6
"The differential operator in calculus is an example of a linear operator."
7
"A linear operator is often represented by a symbol, such as T or A."
8
"A linear operator can be defined in terms of its action on basis vectors."
9
"The identity operator is a special case of a linear operator."
10
"The null operator is a linear operator that maps every vector to zero."
11
"A linear operator preserves the linear structure of a vector space."
12
"A linear operator can have both a domain and a codomain."
13
"A linear operator is sometimes called a linear transformation or a linear mapping."
14
"Eigenvalues and eigenvectors are important concepts in the study of linear operators."
15
"The adjoint operator is the operator that can be used to represent the Hermitian conjugate of a linear operator."
16
"A linear operator is continuous if and only if it is bounded."
17
"The inverse of a bijective linear operator is also a linear operator."
18
"A linear operator is injective if and only if its null space contains only the zero vector."
19
"The range of a linear operator is a subspace of its codomain."
20
"The tensor product of two linear operators is also a linear operator."
1
"A linear operator is an important concept in linear algebra."
2
"The identity operator is a simple example of a linear operator."
3
"A linear operator can be represented by a matrix in certain cases."
4
"The inverse of a linear operator exists if and only if it is bijective."
5
"Eigenvalues and eigenvectors are often studied in the context of linear operators."
6
"The composition of linear operators is itself a linear operator."
7
"In functional analysis, bounded linear operators play a key role."
8
"A linear operator can be defined on a vector space."
9
"The range and null space of a linear operator are important subspaces."
