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II.—On some Transformations connecting General Determinants with Continuants

Published online by Cambridge University Press:  06 July 2012

Thomas Muir
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Extract

§1. It is well known that by a simple transformation of a determinant we may cause a zero to take the place of any one of the elements. The theorems of Hermite and Horner, for example, for depressing the order of a determinant may each of them be viewed as the result of repeated transformations of this kind, the operation being continued until all the elements of a row or column except one are replaced by zeros.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 30 , Issue 1 , 1881 , pp. 5 - 14
Copyright
Copyright © Royal Society of Edinburgh 1883

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References

page 5 note * Liouville's Journal, xiv. p. 26.

page 5 note † Quart. Journ. of Math., viii. pp. 157–162.

page 9 note * Phil. Mag., 4th ser., vol. v. pp. 446–456.