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Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

For any function f:A->B (where A and B are any sets), the kernel (also called the null space) is defined by Ker(f)={x:x in Asuch thatf(x)=0}, so the kernel gives the elements ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

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 ...

Two or more functions, equations, or vectors f_1, f_2, ..., which are not linearly dependent, i.e., cannot be expressed in the form a_1f_1+a_2f_2+...+a_nf_n=0 with a_1, a_2, ...

Fredholm's theorem states that, if A is an m×n matrix, then the orthogonal complement of the row space of A is the null space of A, and the orthogonal complement of the ...

The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...