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Two vectors u and v are parallel if their cross product is zero, i.e., uxv=0.

A 1×n matrix [a_(11) a_(12) ... a_(1n)].

The scalar |v|=ds/dt, where s is the arc length, equal to the magnitude of the velocity v.

A vector field on a circle in which the directions of the vectors are all at the same angle to the circle.

The magnitude (length) of a vector x=(x_1,x_2,...,x_n) is given by |x|=sqrt(x_1^2+x_2^2+...+x_n^2).

If the first nonzero component of the vector difference A-B is >0, then A≻B. If the first nonzero component of A-B is <0, then A≺B.

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

A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...