Matrix arithmetic: Addition, subtraction and scalar multiplication

Adding and subtracting matrices

If two matrices have the same order, it is possible that they can be added to or subtracted from each other. This is done by adding or subtracting the corresponding elements in the matrices.


Given these two matrices and B,

addition - Copy

Adding them would result in:


Multiplying matrices by a number (scalar multiplication)

The act of multiplying a matrix by a number is called scalar multiplication. This is because effectively each element in the matrix is scaled (multiplied) by the number. For example, multiplying a matrix by 3 triples each element in the matrix.



The zero matrix

A matrix with all its elements equal to zero is called a zero matrix. The order of these matrices do not matter, as long as all the elements are zero. The symbol O is used to represent a zero matrix.

zero matrixSee also: