ColorMatrix

When converting from RGB to YUV and vice versa there are multiple sets of coefficients that can be used. The most common are Rec.709, FCC, Rec.601 (aka SMPTE 170M or ITU-R BT.470-2), and SMPTE 240M. The purpose of ColorMatrix is to recalculate the values of a YUV video that has been converted from RGB using one set of coefficients to what the values would be had it been converted from RGB using a different set of coefficients.
The reason this is useful is that MPEG-2 streams typically use Rec.709, whereas most computer software (XviD/DivX decoders, etc...) assumes Rec.601. Thus, if you take an MPEG-2 stream using Rec.709 and pass it as YUV to a decoder which upsamples to RGB using Rec.601 the colors will be slightly off.
In this case, you could use ColorMatrix to convert the video from Rec.709 to Rec.601 and then pass it to the decoder. Another example is if you capture video with software that uses Rec.601 and then want to encode it to MPEG-2 using an encoder that assumes Rec.709.
At first glance, it would appear that to accomplish its task ColorMatrix would need to internally convert to RGB using the source coefficients and then convert back to YUV using the new coefficients. However, this is not the case. What colormatrix actually does is compute the inverse matrix of the source coefficients (gives a matrix for doing YUV->RGB) and then multiplies that matrix with the new coefficient matrix. This gives a set of coefficients for doing the conversion directly from YUV to YUV.
The ColorMatrix filter supports YV12 and YUY2 colorspaces, and can convert between Rec.709, FCC, Rec.601, and SMPTE 240M. ColorMatrix also has the ability to do range expansion and contraction ([16,235/240]->[0,255] or [0,255]->[16,235/240]) as part of the colorimetry conversion or on its own.System requirementsAviSynth 2.0 or higher