# Triangular summation method

From Encyclopedia of Mathematics

A matrix summation method defined by a triangular matrix

that is, by a matrix for which for . A triangulation summation method is a special case of a row-finite summation method. A triangular matrix is called normal if for all . The transformation

realized by a normal triangular matrix has an inverse:

where is the inverse of . This fact simplifies the proof of a number of theorems for matrix summation methods determined by normal triangular matrices. Related to the triangular summation methods are, e.g., the Cesàro summation methods and the Voronoi summation method.

#### References

[1] | G.H. Hardy, "Divergent series" , Clarendon Press (1949) |

[2] | R.G. Cooke, "Infinite matrices and sequence spaces" , Macmillan (1950) |

[3] | S.A. Baron, "Introduction to the theory of summability of series" , Tartu (1966) (In Russian) |

**How to Cite This Entry:**

Triangular summation method.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Triangular_summation_method&oldid=15775

This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article