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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.

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Proceedings
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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.