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Zeros and Periodicity of Functions of Infinite Matrices

Published online by Cambridge University Press:  20 January 2009

Shafik Asaad Ibrahim
Shafik Asaad Ibrahim
Affiliation:
Birkbeck College, University of London
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Extract

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Certain functions of infinite matrices are known to exist.† This gives rise to the following questions:

1. Whether the power series of matrices

has a zero in the field ‡ of infinite matrices, and

2. If f(A) exists for a certain infinite matrix A, is there an infinite matrix B such that

In other words, is there a matrix period for f(A)?

In this paper theorems concerning zeros and periodicity of functions of semi block infinite matrices § (defined below) are established.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 11 , Issue 4 , November 1959 , pp. 225 - 229
Copyright
Copyright © Edinburgh Mathematical Society 1959

References

REFERENCES

Cooke, R. G., Infinite Matrices and Sequence Spaces (Macmillan), 1950.Google Scholar
Ibrahim, S. A. (Ph.D. Thesis, University of London, 1955).Google Scholar
Ibrahim, S. A., Structure of infinite matrices, J. London Math. Soc, 34 (1959), 281–288.CrossRefGoogle Scholar
Wedderburn, J. H. M., Lectures on Matrices, Amer. M.S. Colloquium Publications xvii (New York), 1934.Google Scholar