What is an Elementary Matrix

Elementary Matrix

In mathematics, an elementary matrix is nothing but a matrix obtained by performing only one elementary transformation. They can be denoted as follows:

1. Elementary matrix obtained by interchanging i, jth rows of I is denoted by Eij.
2. Elementary matrix obtained by multiplying ith row of I with non-zero constant K is denoted by Ei (k)
3. Elementary matrix obtained by adding products of elements of jth row of I and a constant m is added to the corresponding elements of ith row, is denoted by Eij(m).