Glossary - A

All terms beginning with the letter 'A' are shown below:

Adjugate (or classical adjoint):	The matrix adj A formed from a square matrix A by replacing the .i; j /-entry of A by the .i; j /-cofactor, for all i and j , and then transposing the resulting matrix.
Afﬁne combination:	A linear combination of vectors (points in Rn ) in which the sum of the weights involved is 1.
Afﬁne dependence relation:	An equation of the form c1 v1 C ! ! ! C cp vp D 0, where the weights c1 ; : : : ; cp are not all zero, and c1 C ! ! ! C cp D 0.
Afﬁne hull (or afﬁne span) of a set S:	The set of all afﬁne combinations of points in S , denoted by aff S.
Afﬁnely dependent set:	A set fv1 ; : : : ; vp g in Rn such that there are real numbers c1 ; : : : ; cp , not all zero, such that c1 C ! ! ! C cp D 0 and c1 v1 C ! ! ! C cp vp D 0.
Afﬁnely independent set:	A set fv1 ; : : : ; vp g in Rn that is not afﬁnely dependent.
Afﬁne set (or afﬁne subset):	A set S of points such that if p and q are in S , then .1 " t/p C t q 2 S for each real number t.
Afﬁne transformation:	A mapping T W Rn ! Rm of the form T .x/ D Ax C b, with A an m # n matrix and b in Rm.
Algebraic multiplicity:	The multiplicity of an eigenvalue as a root of the characteristic equation.
Angle (between nonzero vectors u and v in R2 or R3/:	The angle # between the two directed line segments from the origin to the points u and v. Related to the scalar product by u ! v D kuk kvk cos #
Associative law of multiplication:	A.BC/ D .AB/C , for all A, B, C.
attractor (of a dynamical system in R2):	The origin when all trajectories tend toward 0.
Augmented matrix:	A matrix made up of a coefﬁcient matrix for a linear system and one or more columns to the right. Each extra column contains the constants from the right side of a system with the given coefﬁcient matrix.
Auxiliary equation:	A polynomial equation in a variable r, created from the coefﬁcients of a homogeneous difference equation.