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I.—The Law of Extensible Minors in Determinants

Published online by Cambridge University Press:  06 July 2012

Thomas Muir
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Extract

§1. As a preliminary to the establishment of the law in question, it is necessary to state and exemplify another law to which I have elsewhere directed attention, viz.,

THE LAW OF COMPLEMENTARIES.

To every general theorem which takes the form of an identical relation between a number of the minors of a determinant or between the determinant itself and a number of its minors, there corresponds another theorem derivable from the former by merely substituting for every minor its cofactor in the determinant, and then multiplying any term by such a power of the determinant as will make the terms of the same degree.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 30 , Issue 1 , 1881 , pp. 1 - 4
Copyright
Copyright © Royal Society of Edinburgh 1883

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References

* I do not know who was the first discoverer of this law. It presented itself to me when correcting the proof of my paper on “General Theorems in Determinants” (Trans. Roy. Soc. Edin. 1879). But it must have been known to Professor Cayley before then, for in a note to a paper by Professor Tanner (Mess, of Math. 1878), he refers to it as a means by which Professor Tanner's corresponding law for Pfaffians might be established.