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Schweins's Theorem


If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, and second in terms of the minors of order m formed from any m columns (r<m), with their complementaries; then the sum of the (n-r)_(m-r) terms of the second expansion which have in common the elements in the intersection of the selected r rows and m columns is equal to the sum of the m_r terms of the first expansion which have for one factor the minors of the rth order formed from the elements in the intersection of the selected r rows and m columns.


See also

Determinant, Determinant Expansion by Minors, Minor

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References

Muir, T. "Schweins's Theorem." §141 in A Treatise on the Theory of Determinants. New York: Dover, pp. 124-125, 1960.

Referenced on Wolfram|Alpha

Schweins's Theorem

Cite this as:

Weisstein, Eric W. "Schweins's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchweinssTheorem.html

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