direct sum
- noun
- Specialized
:
suma directa
- The direct sum of two linear spaces may also be "geometrically" described as the Cartesian product of the two individual linear spaces.
Examples
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On the other hand, the dimension of the direct sum is d1 + d2.
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In linear algebra, the direct sum of two disjoint vector spaces creates a new space formed by adding the corresponding vectors from each space.
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And here the direct sum refers to the fact that every.
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And yes, if one talks about one marble, e.g., in the double-slit experiment, it has more possibilities where it can correspond to extending the spaces as a direct sum.
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To find the dimension of the entire space, calculate the dimensions of each space and then take their direct sum.
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The concept of direct sum allows us to combine multiple smaller spaces into a larger one while maintaining their independence.
Synonyms
A way in math to join objects into one while keeping their items separate, like putting two sets together
Surface Forms
Morphology
Although the constituents 'direct' and 'sum' are individually transparent, the precise mathematical meaning — combining disjoint spaces so each element is a tuple/sum of components from each space — is technical and not predictable for an average B1 learner who only knows the common senses of the words. The expression is therefore partially compositional (the words give a general sense of a special kind of sum and many languages calque this term) but its technical constraints and formal interpretation make it not fully transparent.
Etymology
The term direct sum gives a simple picture: take one item from each of two separate boxes and join them side by side; the joining is the sum and it is done in a direct way. So a direct sum in math means 'to add' two separate sets by pairing one item from each so every new item comes from both parts, not from mixing them.
