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An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...

A vector space V with a ring structure and a vector norm such that for all v,W in V, ||vw||<=||v||||w||. If V has a multiplicative identity 1, it is also required that ...

The parallelogram law gives the rule for vector addition of vectors A and B. The sum A+B of the vectors is obtained by placing them head to tail and drawing the vector from ...

A collection of faces of an n-dimensional polytope or simplicial complex, one of each dimension 0, 1, ..., n-1, which all have a common nonempty intersection. In normal three ...

An invertible linear transformation T:V->W is a map between vector spaces V and W with an inverse map which is also a linear transformation. When T is given by matrix ...

The term used in physics and engineering for a harmonic function. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a ...

A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...