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Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where ...

A variable that may assume only real values.

A beautiful class of polyhedra composed of rhombic faces discovered accidentally by R. Towle while attempting to develop a function to create a rhombic hexahedron from a ...

Let H be a subgroup of G. A subset T of elements of G is called a right transversal of H if T contains exactly one element of each right coset of H.

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

A straightedge with markings to indicate distances. Although geometric constructions are sometimes said to be performed with a ruler and compass, the term straightedge is ...

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.

An analytic function f on the unit disk is called schlicht if 1. f is one-to-one, 2. f(0)=0, and 3. f^'(0)=1, in which case it is written f in S. Schlicht functions have ...

There are at least two statements known as Schur's lemma. 1. The endomorphism ring of an irreducible module is a division algebra. 2. Let V, W be irreducible (linear) ...

D = f_(xx)f_(yy)-f_(xy)f_(yx) (1) = f_(xx)f_(yy)-f_(xy)^2, (2) where f_(ij) are partial derivatives.