This is part of my filter effects tutorial series
Convolve Matrix can be used for several different effects like blurring, sharpening, edge detection and embossing. While it's a powerful tool, it can take quite some expertise to create the desired effect.
Inkscape support for Convolve Matrix filter primitive is not yet quite finished, but it can already be used for some work. The biggest problem is, the results will depend on the rendering resolution.
The idea of this filter is to apply a convolution on image. Basically, it takes certain amount of pixels around the target pixel, multiplies the colour values of each pixel by its multiplier and sums them up to form new colour value for the target pixel. There also exists common divisor and bias that will be applied after summing pixel values up.
For more through and mathematical explanations of convolutions, see Wikipedia page on Convolutions or article on Matrix convolution filters on GameDev.net.
Here's an graphical example with single target pixel and the 3×3 area surrounding it.
This same filter is specified in Inkscape Filter Effects dialog as follows:
Two special notes here: first of all, the bias is specified as 128 in the first image but as 0.5 in second image. These are actually the same thing, the first image just uses colour values in range 0–255, the second image in range 0–1.
Second, the divisor isn't actually required. I could have specified the kernel with values of -1/8 and 1.0 and left the divisor as one. The divisor just makes specifying the values easier.
Here are some examples of possible effects:
(notice though: usually it's better to use the Gaussian Blur filter primitive for blurring)