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A Method of Evaluating Certain Determinants
Published online by Cambridge University Press: 20 January 2009
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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
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