Matrix minor: definition, example

In this publication, we will consider what a matrix minor is, how it can be found, and also analyze an example to consolidate the theoretical material.

Matrix minor definition

Minor M_ij to element a_ij the determiner n-th order is the determinant (N-1)-th order, which is obtained by deleting the line i and column j from source.

basic any non-zero minor of a matrix of maximum order is called. Those. in the matrix A order minor r is basic if it does not equal zero, and all minors of order r+1 and above are either zero or do not exist. In this way, r matches the smaller of the values m or n.

An example of finding a minor

Let’s find a minor M₃₂ to element a₃₂ definer below:

Solution

According to the task, we need to delete the third row and the second column from the determinant:

We get this result:

For the same determinant minor M₁₃ to element a₁₃ looks like that: