Minor

Every element in a matrix has a minor. The minor of an element is the determinant of a smaller matrix that eliminates the row and column of the element. For example, consider a 3 x 3 matrix—what is the minor of element 2, 1?

First, eliminate row 2 and column 1 from the matrix. This will result in a smaller 2 x 2 matrix. The determinant of this 2 x 2 matrix is the minor of element 2, 1. The following diagram demonstrates this:

Figure 3.6: The minor of element 2, 1 in a 3 x 3 matrix

This formula works for higher-dimension matrices as well. For example, the minor of an element in a 4 x 4 matrix is the determinant of some smaller, 3 x 3 matrix. A matrix of minors is a matrix where every element is the minor of the corresponding element from the input matrix.