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The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

A vector difference is the result of subtracting one vector from another. A vector difference is denoted using the normal minus sign, i.e., the vector difference of vectors A ...

Given vectors u and v, the vector direct product, also known as a dyadic, is uv=u tensor v^(T), where tensor is the Kronecker product and v^(T) is the matrix transpose. For ...

In general, there is no unique matrix solution A to the matrix equation y=Ax. Even in the case of y parallel to x, there are still multiple matrices that perform this ...

A function of one or more variables whose range is three-dimensional (or, in general, n-dimensional), as compared to a scalar function, whose range is one-dimensional. Vector ...

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

Let theta be the angle between two vectors. If 0<theta<pi, the vectors are positively oriented. If pi<theta<2pi, the vectors are negatively oriented. Two vectors in the plane ...

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

The span of subspace generated by vectors v_1 and v_2 in V is Span(v_1,v_2)={rv_1+sv_2:r,s in R}. A set of vectors m={v_1,...,v_n} can be tested to see if they span ...