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A square matrix A is called diagonally dominant if |A_(ii)|>=sum_(j!=i)|A_(ij)| for all i. A is called strictly diagonally dominant if |A_(ii)|>sum_(j!=i)|A_(ij)| for all i. ...

Any lemma on commutative diagrams. It can give relations between maps (as in the five lemma) or tell how to construct new diagrams from old ones (as in the snake lemma).

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0) in the direction u. It is a vector form of the ...

The divergence theorem, more commonly known especially in older literature as Gauss's theorem (e.g., Arfken 1985) and also known as the Gauss-Ostrogradsky theorem, is a ...

The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest ...

Let P be a matrix of eigenvectors of a given square matrix A and D be a diagonal matrix with the corresponding eigenvalues on the diagonal. Then, as long as P is a square ...

An equalizer of a pair of maps f,g:X->Y in a category is a map e:E->X such that 1. f degreese=g degreese, where degrees denotes composition. 2. For any other map e^':E^'->X ...

A functor between categories of groups or modules is called exact if it preserves the exactness of sequences, or equivalently, if it transforms short exact sequences into ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...