| slovo | definícia |
inner product
(encz) | inner product, n: |
inner product
(wn) | inner product
n 1: a real number (a scalar) that is the product of two vectors
[syn: scalar product, inner product, dot product] |
inner product
(foldoc) | inner product
In linear algebra, any linear map from a
vector space to its dual defines a product on the vector
space: for u, v in V and linear g: V -> V' we have gu in V' so
(gu): V -> scalars, whence (gu)(v) is a scalar, known as the
inner product of u and v under g. If the value of this scalar
is unchanged under interchange of u and v (i.e. (gu)(v) =
(gv)(u)), we say the inner product, g, is symmetric.
Attention is seldom paid to any other kind of inner product.
An inner product, g: V -> V', is said to be positive definite
iff, for all non-zero v in V, (gv)v > 0; likewise negative
definite iff all such (gv)v < 0; positive semi-definite or
non-negative definite iff all such (gv)v >= 0; negative
semi-definite or non-positive definite iff all such (gv)v |
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