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The shear matrix e_(ij)^s is obtained from the identity matrix by inserting s at (i,j), e.g., e_(12)^s=[1 s 0; 0 1 0; 0 0 1]. (1) Bolt and Hobbs (1998) define a shear matrix ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

Let C be a category. Then D is said to be a subcategory of C, if the objects of D are also objects of C, if the morphisms of D are also morphisms of C, and if D is a category ...

A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is ...

An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.

The Woodbury formula (A+UV^(T))^(-1)=A^(-1)-[A^(-1)U(I+V^(T)A^(-1)U)^(-1)V^(T)A^(-1)] is a formula that allows a perturbed matrix to be computed for a change to a given ...

A zero function is a function that is almost everywhere zero. The function sometimes known as "the zero function" is the constant function with constant c=0, i.e., f(x)=0 ...

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

A zero vector, denoted 0, is a vector of length 0, and thus has all components equal to zero. It is the additive identity of the additive group of vectors.

A q-analog of the multinomial coefficient, defined as ([a_1+...+a_n]_q!)/([a_1]_q!...[a_n]_q!), where [n]_q! is a q-factorial.