# Multiply matrices in Processing

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Posted May 24 2010 08:18 AM

A matrix is a 2 dimensional array of numbers called elements. Matrices are used in many different applications, representing sets of equations, transformations to 3D objects, or color filters, to name just a few. This Answer explains how multiply two matrices in Processing.

First, a matrix is usually characterized by its dimensions: the number of elements in its rows (the numbers going across ) and columns (the numbers going up and down). By convention, the number of rows always comes first. The following figure shows a 2 row by 3 matrix, which is generally just called a 2x3 matrix, and a 3x2 matrix:

To multiply two matrices together (lets call them A and B), the number of columns in A must equal the number of rows in B. This is critical -- if this isn't true, then the multiplication is not defined. (This is sort of like dividing by zero -- it's simply impossible.)

Assuming this criteria is met, the product of the two matrices (lets call it C) will have the same number of rows as A and the same number of columns as B.
The elements in C are equal to the sum of the products of the corresponding column element in A times the row element in B. This is a bit tricky, but the following figure should (hopefully!) make this a bit clearer:

So, this is great an all, but at this point you're probably wondering "This is great and all, but how do I code this?" The following Processing code sample shows you how:

```
// Create a 2x3 matrix
float[][] A = {
{1.0, 0.0, 0.0},
{1.0, 0.5, 1.0}
};

// Create a 3x2 matrix
float[][] B = {
{2.0, 0.0 },
{1.0, 3.0},
{3.0, 0.5}
};

// Create a 2x2 matrix to hold the product
float[][] C = new float[2][2];  //result matrix

//This section performs the actual multiplication
for (int i=0; i < C.length; i++) { //Loop through each row in C
for (int j=0; j < C[0].length; j++) {  //Loop through each col in C
for (int k=0; k < B.length; k++) {
//The element C[i][j] is the sum of the products of the row in A * the col in C
C[i][j] += A[i][k] * B[k][j];  // that row in A * that col in B
}
}
}

//Print out the results
for (int i=0; i < C.length; i++) {
for (int j=0; j < C[0].length; j++) {
println("[" + i + "][" + j + "] = " + C[i][j]);
}
}

```

On its own, this is not very exciting, but it's the basis for a lot of interesting applications I'll explore in some other Answers.

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