If we expand the determinant of a matrix using determinant expansion by minors, first in terms of the minors of order formed from any rows, with their complementaries, and second in terms of the minors of order formed from any columns (), with their complementaries; then the sum of the terms of the second expansion which have in common the elements in the intersection of the selected rows and columns is equal to the sum of the terms of the first expansion which have for one factor the minors of the th order formed from the elements in the intersection of the selected rows and columns.
Schweins's Theorem
See also
Determinant, Determinant Expansion by Minors, MinorExplore with Wolfram|Alpha
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 TheoremCite this as:
Weisstein, Eric W. "Schweins's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchweinssTheorem.html