ABSTRACT
Matrix multiplication consists of row-element to column-element multiplication and summation of the resulting products. Multiplication of the two matrices A and B is defined only when the number of columns of matrix A is the same as the number of rows of matrix B. Matrices that satisfy this condition are called conformable in the order AB. Thus, if the size of matrix A is n x m and the size of matrix B is m x r, then
AB = [ai,j][bi) = [ci,)] = C ci,i = L ai,kbk,j k=1
(i = I, 2, ... , n, j = I, 2, ... , r) (1.22)
The size of matrix C is n x r. Matrices that are not conformable cannot be multiplied. It is easy to make errors when performing matrix multiplication by hand. It is helpful
to trace across the rows of A with the left index finger while tracing down the columns of B with the right index finger, multiplying the corresponding elements, and summing the products. Matrix algebra is much better suited to computers than to humans.
