Matrix Multiplication in C | Matrix Chain Multiplication Program in C

Matrix Multiplication in C

A is the same as the number of rows in B.

The general definition of matrix multiplication is as follows: If A is a n×m matrix and B is a m×p matrix, their product C will be a n×p matrix such that the general element cij of C is given by


Note that in general AB is not equal to BA (matrix multiplication is not commutative).



Since a vector is simply a one-dimensional matrix, the definition of matrix multiplication given above also applies when a vector is multiplied by an appropriate matrix, e.g.,


The operator * is used for matrix multiplication, as you may have guessed. For example, if

 a =

 1 2

 3 4


 b =

 5 6

 0 -1

the statement

 c = a * b

results in

 c =

 5 4

 15 14

Note the important difference between the array operation a .* b (evaluate by hand and check with MATLAB) and the matrix operation a * b.

To multiply a matrix by a vector in that order, the vector must be a column vector. So if

 b = [2 3]'

the statement