linear functionals 283 浏览 0关注

'may be functional (mathematics)|functionals in the traditional sense of functions of functions, but this is not necessarily the case. In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalar (mathematics)|scalars.&nbsp; In Euclidean space|Rn, if euclidean vector|vectors are represented as column vectors, then linear functionals are represented as row vectors, and their action on vectors is given by the dot product, or the matrix product with the row vector on the left and the column vector on the right.&nbsp; In general, if V is a vector space over a field (mathematics)|field k, then a linear functional ƒ is a function from V to k, which is linear: :f(\vec{v}+\vec{w}) = f(\vec{v})+f(\vec{w}) for all \vec{v}, \vec{w}\in V :f(a\vec{v}) = af(\vec{v}) for all \vec{v}\in V, a\in k. The set of all linear functionals from V to k, Homk(V,k), is itself a vector space over k.&nbsp; This ...
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