Java Script Linear Algebra II
By Marcus Kazmierczak

 

Enter Matrix A:



   

Enter Matrix B :



 

What do you wish to calculate :

Solution Matrix C :



 

The Mathematics Behind It

Let A represent our 3x3 Matrix.

A + B = C The addition of two matrices is straight forward. You just add each matrix position-wise. So the upper-left element of matrix A plus the upper-left element of matrix B is the upper-left element in matrix C. Do the same for all postions.
 
A x B = C

The multiplication of two matrices is not quite as simple. First we need the matrices to be of proper size. This means matrix A sizen x m must be multiplied by a mx p matrix. The resultant matrix will then be n x p. For our case, we are using two 3x3 matrices, so this isn't a problem.

The equation for multiplying two matrices is : (elementwise)

[AB]ij = Ê [A]ik[B]kj

where the Ê summation goes from k=1...n

 

A example element from our 3x3 Case. To get the first element in our solution matrix c11

c11 = (a11 * b11) + (a12 * b21) + (a13 * b31)

where aij and bij are from matrices A, B respectively.

 

 

On To : Java Script Linear Algebra Page III

 

E-Mail : marcus@mkaz.com