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, j^th rows of I is denoted by E_ij.
2. Elementary matrix obtained by multiplying i^th row of I with non-zero constant K is denoted by E_i (k)
3. Elementary matrix obtained by adding products of elements of j^th row of I and a constant m is added to the corresponding elements of i^th row, is denoted by E_ij(m).