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The Sum of the Signed Primary Minors of a Determinant

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

(1) The fundamental propositions in regard to the sum of the signed primary minors of a determinant are—

(A) An expression for the negative sum of the signed primary minors of any determinant is got by taking a determinant of the next higher order whose first element is zero with the given determinant for complementary minor, and whose remaining elements are units all positive or all negative.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 25 , Issue 1 , 1906 , pp. 372 - 382
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

page 372 note * Proceedings Roy. Soc. Edinburgh, xxiv. pp. 387-392.

page 380 note * By Dr F. S. Macaulay in Math. Gazette, iii. pp. 44-45.

page 382 note * Vide my Text-Book of Determinants, p. 173, § 127.