A survey of infinite matrices

Oscar Hernan Estrada, University of Texas at El Paso


The purpose of this work is not to be a comprehensive treatise in the theory of infinite matrices. No attempt has been made to go deeply into any particular aspect of the various subjects; the aim has been to provide a handy explanation of the fundamental ideas at the basis of the special subject, intended for any level of readership at or above the undergraduate, including non-mathematicians. ^ We show the generalization of some of the well-known results in finite matrix theory such as determinants and inverses of matrices. We also present examples of situations which would never occur with finite matrices, as well as an application of infinite matrices to summability theory. ^ The theory of infinite matrices has not been developed to the extent of the finite matrix theory; a proof of this is the fact that there is no book which gather all the known facts about them. The only attempt in this direction has been made by Richard Cooke in his book Infinite Matrices and Sequence Spaces [4], but even here, many results are not presented. Most of the results are scattered all over the literature, but not in one single volume; I have tried to fill this gap by presenting many results in a single paper. Some examples are known and some are of my own; proper references and acknowledgments are given where required. ^ A list of references is given at the end of the work for those who want a deeper knowledge of the subject; some of the books cited on this paper were not necessarily used here, but they appear in order to have a list of books, as complete as possible, for reference. ^

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Recommended Citation

Estrada, Oscar Hernan, "A survey of infinite matrices" (2003). ETD Collection for University of Texas, El Paso. AAIEP10543.