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 ′.

单词	orthogonal sum
释义	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 ′.
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