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A Method of Evaluating Certain Determinants

Published online by Cambridge University Press:  20 January 2009

J. L. Burchnall
J. L. Burchnall
Affiliation:
The University, Durham.
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1. Let [ast] (s, t=0, 1, … n) be a square matrix of order n+1 and determinant |ast| and suppose that by repeated “isolation” of the variables the corresponding bilinear form has been expressed as

where, for all r,

Then

Now (1) implies, and is implied by, the identities

Thus, from any known identity of the form (4), subject to the condition (2), we may at once infer, using (3). the value of the corresponding determinant |ars|.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 2 , November 1954 , pp. 100 - 104
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

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