The matrices entered in the left bar have been simplifed to the following $ \begin{aligned} (3 \times 3) \end{aligned} $ matrix plus the addition of a $ \begin{aligned} (3 \times 1) \end{aligned} $ matrix or vector.

We can now expand this to show the actual calculations that will be made when this formula is applied to points in an image. The following is the matrix when multiplied by the $ \begin{aligned} (x, y, z) \end{aligned} $ varibles. These represent every point in a mesh or it could be a single point in 3d space.

The following is the final result, when we include the addition of the $ \begin{aligned} (3 \times 1) \end{aligned} $ matrix(vector) to the previously calculated $ \begin{aligned} (3 \times 1) \end{aligned} $ matrix.

Note that the $ \begin{aligned} (x, y, z) \end{aligned} $ is a point, and the calculation is applied to every point in a mesh, to produce the new $ \begin{aligned} (x', y', z') \end{aligned} $ points. These points will be rotated, translated or scaled based on the calculations.

Try adding a matrix or vector with the buttons below the list on the left. They can be removed by clicking the 'x' in the top left on each matrix in the list. Experiment with dragging the matrices to change their order in the list.

Experiment also with the inputs of the matrices cells. They will accept expressions like $ \begin{aligned} 3 * (0.1 + 10) \end{aligned} $ and even scary but the useful trigonometric functions like $ \begin{aligned} sin(45) \end{aligned} $ or $ \begin{aligned} cos(90) \end{aligned} $ and do all the calculations for you.