Glossary  F
All terms beginning with the letter 'F' 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. 
Field:  A field is a set 𝔽 with at least two elements together with a function 𝔽 × 𝔽 ⇾ 𝔽 called addition, denoted (a, b) → a + b, and a function 𝔽 × 𝔽 ⇾ 𝔽 called multiplication, denoted (a, b) → ab, which satisfy the following axioms:

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. 