I am learning about the Convolution Matrix, and I understand how they work, but I don't understand how to know before hand what the output of a Matrix will look like. For example lets say I want to add a blur to an image, I could guess 10,000+ different combinations of numbers before I get the correct one.

I do know though that this formula will give me a blur effect, but I have no idea why.

float[] sharpen = new float[] {
     1/9f, 1/9f, 1/9f,
     1/9f, 1/9f, 1/9f,
     1/9f, 1/9f, 1/9f
};

Can anyone either explain to me how this works or point me to some article, that explains this? I would like to know before hand what a possible output of the matrix will be without guessing.

Basically I would like to know why do we put that number in the filed, and why not some other number?