Computation of the Adjoint Matrix

The best method for computing the adjoint matrix of an order $n$ matrix in an arbitrary commutative ring requires $O(n^{β+1/3}\log n \log \log n)$ operations, provided the complexity of the algorithm for multiplying two matrices is $γn^β+o(n^β)$. For a commutative domain -- and under the same assumptions -- the complexity of the best method is ${6γn^β}/{(2^β-2)}+o(n^β)$. In the present work a new method is presented for the computation of the adjoint matrix in a commutative domain. Despite the f...