Let $n$ be a \reftext{def:natural-numbers-2026a}{natural number} with $n\ge 2$, and let $A=(a_{ij})_{1\le i,j\le n}$ be an $n\times n$ real matrix.

For indices $i,j\in\{1,\dots,n\}$, the $(i,j)$ \textit{minor} of $A$, denoted $M_{ij}(A)$, is the \reftext{def:determinant-real-square-matrix-2026a}{determinant} of the $(n-1)\times(n-1)$ real matrix obtained from $A$ by deleting row $i$ and column $j$.

The $(i,j)$ \textit{cofactor} of $A$ is

The \textit{adjugate} matrix of $A$ (also called the classical adjoint) is the $n\times n$ real matrix

i.e., the matrix whose $(i,j)$ entry is the $(j,i)$ cofactor of $A$.