orthogonal sum

orthogonal sum

[ȯr¦thäg·ən·əl ′səm]
(mathematics)
A vector space E with a scalar product is said to be the orthogonal sum of subspaces F and F ′ if E is the direct sum of F and F ′ and if F and F ′ are orthogonal spaces.
A scalar product g on a vector space E is said to be the orthogonal sum of scalar products ƒ and ƒ′ on subspaces F and F ′ if E is the orthogonal sum of F and F ′ (in the sense of the first definition) and if g (x + x ′, y + y ′) = ƒ(x, y) + ƒ′(x ′, y ′) for all x, y in F and x ′, y ′ in F ′.
References in periodicals archive ?
The harmonic 1-forms split into an orthogonal sum of holomorophic and anti-holomorphic 1-forms corresponding to the -i and +i eigenspaces of the Hodge star operator.
The orthogonal sum of the evidence from two sources operates by sequentially multiplying the evidence for a given source class, by the evidence of each class of the following source (2.
The orthogonal sum of two evidence vectors, m1 and m2, is denoted by m1 [direct sum] m2.

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