When we have two matrices, and then the matrix subtraction or matrix difference is a matrix whose entry is formed by subtracting the corresponding entry of from each entry of , that is .
Matrix subtraction works only when the two matrices have the same size and the result is also the same size as the input matrices.
The interactive program below shows you the result of matrix subtraction. Your input must be two matrices of the same size (one matrix for each text box). Random Example will generate random matrices of the same size.
Some important properties of matrix difference are
- Matrix subtraction is a non-commutative operation. If you reverse the order you will not get the same result
- Null matrix (or zero matrix) is a unique difference identity matrix such that . The null matrix has the same size as matrix .
- We can define a negative of (written as ) such that matrix addition with the negative will produce a null matrix ,