## Jacobi's Theorem

Let be an -rowed Minor of the th order Determinant associated with an Matrix in which the rows , , ..., are represented with columns , , ..., . Define the complementary minor to as the -rowed Minor obtained from by deleting all the rows and columns associated with and the signed complementary minor to to be

Let the Matrix of cofactors be given by

with and the corresponding -rowed minors of and , then it is true that

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, pp. 1109-1100, 1979.