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An exclusion theorem for tri-diagonal matrices

Published online by Cambridge University Press:  20 January 2009

John W. Jayne
John W. Jayne
Affiliation:
United States Naval Academy, AnnapolisMaryland—21402, U.S.A.
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An n × n matrix An = (aij) is tri-diagonal if aij = 0 for |i−j|≧2. The latent roots of such matrices may be conveniently studied by forming the sequence of polynomials Ψk(λ)=|λI−Ak|, where Ak is the principal submatrix of Ak+1 obtained by deleting the last row and column of Ak+1, and then observing that these polynomials satisfy the following recurrence relation:

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 3 , June 1969 , pp. 251 - 253
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Arscott, F. M.Latent roots of tri-diagonal matrices, Edinburgh Math. Notes, 44, 5–7 [in Proc. Edinburgh Math Soc. 12 (1961)].CrossRefGoogle Scholar
(2)Marcus, M. and Minc, H.A Survey of Matrix Theory and Matrix Inequalities (Allyn and Bacon, 1964).Google Scholar
(3)Schneider, H. (editor), Recent Advances in Matrix Theory (Univ. of Wisconsin Press, 1964).Google Scholar