direct sum Synonyms
No Synonyms and anytonyms found
direct sum Meaning
direct sum (n)
a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets
direct sum Sentence Examples
- The direct sum of two subspaces is the set of all vectors that can be written as a sum of two vectors, one from each subspace.
- The direct sum of two vector spaces is a new vector space that is formed by combining the two vector spaces and defining a new addition operation.
- The direct sum of a sequence of vector spaces is the vector space that is formed by taking the direct sum of the first two vector spaces, then taking the direct sum of that result with the third vector space, and so on.
- The direct sum of two matrices is the matrix that is formed by stacking the two matrices on top of each other.
- The direct sum of two modules is the module that is formed by taking the direct sum of the underlying abelian groups.
- The direct sum of two algebras is the algebra that is formed by taking the direct sum of the underlying vector spaces and defining a new multiplication operation.
- The direct sum of two fields is the field that is formed by taking the direct sum of the underlying sets and defining a new addition and multiplication operation.
- The direct sum of two rings is the ring that is formed by taking the direct sum of the underlying sets and defining a new addition and multiplication operation.
- The direct sum of two ordered sets is the ordered set that is formed by taking the direct sum of the underlying sets and defining a new ordering relation.
- The direct sum of two complete metric spaces is the complete metric space that is formed by taking the direct sum of the underlying sets and defining a new metric.
FAQs About the word direct sum
a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets
No synonyms found.
No antonyms found.
The direct sum of two subspaces is the set of all vectors that can be written as a sum of two vectors, one from each subspace.
The direct sum of two vector spaces is a new vector space that is formed by combining the two vector spaces and defining a new addition operation.
The direct sum of a sequence of vector spaces is the vector space that is formed by taking the direct sum of the first two vector spaces, then taking the direct sum of that result with the third vector space, and so on.
The direct sum of two matrices is the matrix that is formed by stacking the two matrices on top of each other.
