given matrices $A$ and $B$ in a ring $R$ of sizes $m \times n$ and $n \times m$ we have $\det (AB) = \sum \det (A_ S)\det ({}_ SB)$ in $R$ where the sum is over subsets $S \subset \{ 1, \ldots , n\} $ of size $m$ and $A_ S$ is the $m \times m$ submatrix of $A$ with columns corresponding to $S$ and ${}_ SB$ is the $m \times m$ submatrix of $B$ with rows corresponding to $S$,
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)