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The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

A closed interval corresponding to a finite portion of an infinite line. Line segments are generally labeled with two letters corresponding to their endpoints, say A and B, ...

A number of points on a line segment. The term was first used by Desargues (Cremona 1960, p. x). If the points A, B, C, ... lie on a line segment with the coordinates of the ...

A linear algebraic group is a matrix group that is also an affine variety. In particular, its elements satisfy polynomial equations. The group operations are required to be ...

A linear congruence equation ax=b (mod m) (1) is solvable iff the congruence b=0 (mod d) (2) with d=GCD(a,m) is the greatest common divisor is solvable. Let one solution to ...

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. The ...

A linear extension of a partially ordered set P is a permutation of the elements p_1, p_2, ... of P such that p_i<p_j implies i<j. For example, the linear extensions of the ...

In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...