1. A matrix generation apparatus for generating a transformation matrix used for transforming input data into output data using a plurality of pairs of sample data, each pair including pre-transformation sample data and post-transformation sample data, the apparatus comprising: a projection matrix generation means for generating, on the assumption that a first feature space vector generated by projecting the pre-transformation sample data into a feature space by a first projection matrix and a second feature space vector generated by projecting the post-transformation sample data into the feature space by a second projection matrix are substantially identical to each other with respect to each pair of sample data, the first projection matrix and the second projection matrix using the plurality of pairs of sample data; and a transformation matrix generation means for generating a transformation matrix used for transforming the input data into the output data using the first and second projection matrices generated by the projection matrix generation means.