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XI.—The Minors of a Product-Determinant

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

1. If for aα+bβ+cγ+…we put

the the product of |a1b2c3| and |f1g2h3| may be written

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 27 , 1907 , pp. 79 - 87
Copyright
Copyright © Royal Society of Edinburgh 1907

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References

page 79 note * This is usually written but throughout the present paper row-by-column multiplication is used, so as to have the results immediately applicable to matrices.

page 84 note * In the original memoir (Trans. Roy. Soc. Edin., xxxii. pp. 461–482), in which the properties of the functions which represent the elements of product-determinants are investigated, it is stated (p. 481) that they were given the name ‘bipartite’ from Cayley's use of the word for a special set of the functions, namely, those of the third degree. It has often since appeared to me that it would have been preferable to have extended the meaning of another word, namely, the word ‘cumulant,’ this being the name given by Sylvester to a special set of the second order.