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Bi-determinants

Published online by Cambridge University Press:  31 October 2008

H. W. Turnbull
H. W. Turnbull
Affiliation:
University of St Andrews.
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The important Binet-Cauchy theorem of determinants (3, p. 81)

may be illustrated as follows. Consider the identity

where ax = a1x1 + a2x2 + a3x3, and similarly for ay, bx, by. This identity follows by adding x1 row1 + x2row2 + x3row3 to row4 in the first determinant; and y1row1 + etc. to row5. Then by expanding both determinants in a Laplace development of the first three rows and the last two we obtain the identity

.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 30 , January 1937 , pp. xv - xxi
Copyright
Copyright © Edinburgh Mathematical Society 1937

References

REFERENCES

1. Muir : History of Determinants.Google Scholar
2.Muir, and Metzler, (New York, 1930), Theory of Determinants.Google Scholar
3.Turnbull, : Theory of determinants, matrices and invariants (1928).Google Scholar
4.Turnbull, and Aitken, : Canonical Matrices (1932).Google Scholar