Sentences with DIRECT-SUM
Check out our example sentences below to help you understand the context.Sentences
1
"The direct sum of two vectors is denoted by the symbol ⊕."
2
"In linear algebra, the direct sum of vector spaces involves combining them into a larger vector space."
3
"The direct sum of two subspaces is the set of all possible combinations of vectors from each subspace."
4
"For example, the direct sum of R² and R³ is a vector space in R⁵."
5
"The direct sum of two matrices can be calculated by concatenating them horizontally."
6
"The direct sum of three sets is a set that contains all possible combinations of elements from each set."
7
"The direct sum of two groups is a group formed by combining their elements and operations."
8
"In category theory, the direct sum is a categorical construction that generalizes vector space direct sums."
9
"The direct sum of two modules over a ring is a module formed by combining their elements and operations."
10
"The direct sum of two ideals in a ring is defined as the set of all possible sums of elements from each ideal."
11
"In topology, the direct sum of two topological spaces is a new space formed by combining their underlying sets."
12
"Direct summands are the individual components of a direct sum."
13
"Direct sum decompositions are a way of expressing a structure as a direct sum of simpler structures."
14
"The direct sum of two algebras is an algebra formed by combining their underlying vector spaces and operations."
15
"The direct sum of two fields is a larger field that contains both of them as subfields."
16
"Direct sums are often used to define and study direct sum representations in representation theory."
17
"In differential geometry, direct sums can be used to define tensor products of vector bundles."
18
"The direct sum of two graphs is a larger graph formed by combining their vertices and edges."
1
"The direct sum of two vector spaces is a new vector space that is formed by pairing corresponding elements from the original vector spaces and performing component-wise addition."
2
"In mathematics, the direct sum of two groups is a construction that combines the groups into a larger group."
3
"The direct sum of two matrices is a matrix formed by taking corresponding elements and adding them."
4
"A direct sum of modules is a module formed by taking the direct sum of the underlying abelian groups of the modules and defining multiplication accordingly."
5
"The direct sum of two subspaces is the smallest subspace that contains both of them."
6
"To compute the direct sum of two sets, we combine the elements of the sets without repetition."
7
"The direct sum of two graphs is a new graph formed by combining the vertices and edges of the original graphs."
8
"In quantum mechanics, the direct sum of two Hilbert spaces represents the combined state space of two subsystems."
9
"When calculating the direct sum of two abelian groups, we take the Cartesian product of their underlying sets and define group operations component-wise."
10
"The direct sum of two vector bundles is a new vector bundle formed by taking the direct sum of their fibers over each point of the base."
