Examples of 'direct sum' in a sentence
Meaning of "direct sum"
direct sum ~ a mathematical term used to describe the combination of two objects in a specific way
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- coproduct in some categories, like abelian groups, topological spaces or modules
- A linear sum in which the intersection of the summands has dimension zero. Equivalently, a linear sum of two subspaces, any vector of which can be expressed uniquely as a sum of two vectors: one vector belonging to the first subspace, and the other vector belonging to the second subspace.
- A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.
How to use "direct sum" in a sentence
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direct sum
A direct sum of finite cyclic groups is periodic.
Underlying vector space is the direct sum.
Direct sum of a vector of matrices.
The right hand side is a direct sum of fields.
The direct sum decomposition is usually referred to as gradation or grading.
Any projection is associated with a direct sum decomposition.
Every direct sum of finitely many injective modules is injective.
The general case is a direct sum of these two cases.
Direct sum of vector bundles.
Another example is the direct sum of all dihedral groups.
Direct sum or direct product.
A homogeneous ideal is the direct sum of its homogeneous parts.
Direct sum of matrices.
Internal direct sum.
The direct sum of abelian groups is a prototypical example of a direct sum.
See also
External direct sum.
Direct sum of modules.
Orthogonal direct sum.
V is a direct sum of simple modules.
Representations of the rotation group into a direct sum of irreducible representations.
Direct sum of rings.
This means that every representation reduces to a direct sum of irreducible representations.
Which is a direct sum of the kernel and the image.
In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum.
Thus the direct sum is the coproduct in the appropriate category.
The cup product gives a multiplication on the direct sum of the cohomology groups.
The locally convex direct sum and inductive limit of bornological spaces is bornological.
Every representation of the multiplicative group Gm is a direct sum of irreducible representations.
The direct sum with this norm is again a Banach space.
The exterior product endows the direct sum of these groups with a ring structure.
The direct sum of a finite number of Fréchet spaces is a Fréchet space.
A local Grover iteration is a direct sum of Grover iterations over each block.
The eigenspaces of T always form a direct sum.
The matricial direct sum calculates the sum of N matrices that can be of different sizes.
A symmetric Lie algebra decomposes into the direct sum of its socle and cosocle.
Direct sum of Lie algebras.
This proves that B is the direct sum of im q and ker t.
Direct sum of Banach spaces.
Additionally, the direct sum of binary matroids is binary.
Direct sum of Hilbert spaces.
A representation is called isotypic, if it is a direct sum of isomorphic, irreducible representations.
A direct sum of simple Lie algebras is called a semisimple Lie algebra.
In this situation, a representation need not be a direct sum of irreducible representations.
The criteria proposed Table 4 are based on a scoring system of direct sum.
More generally, a direct sum of torsionless modules is torsionless.
That means, the representation space is decomposed into a direct sum of its isotypes.
Thus, a reductive Lie algebra is a direct sum of a commutative algebra and a semisimple algebra.
A finite dimensional C * - algebra A is canonically isomorphic to a finite direct sum.
The Kronecker sum is different from the direct sum but is also denoted by ⊕.
Instead, it may be a direct sum of several representations that are irreducible for Sn - 1.
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Examples of using Sum
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The purchase sum was to be paid in three instalments
Private cofinancing is the sum of the two
This sum of money is all for you
Examples of using Direct
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Direct purchases of equipment are the most obvious
There was not a direct line to the continent
Direct beneficiaries of mine risk education were reached
