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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 ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

Strong convergence is the type of convergence usually associated with convergence of a sequence. More formally, a sequence {x_n} of vectors in a normed space (and, in ...

In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...

Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition.

The Lie derivative of tensor T_(ab) with respect to the vector field X is defined by L_XT_(ab)=lim_(deltax->0)(T_(ab)^'(x^')-T_(ab)(x))/(deltax). (1) Explicitly, it is given ...

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 ...