  A matrix-compression algorithm is derived from a novel isogenic block
decomposition for square matrices. The resulting compression and inflation
operations possess strong functorial and spectral-permanence properties. The
basic observation that Hadamard entrywise functional calculus preserves
isogenic blocks has already proved to be of paramount importance for
thresholding large correlation matrices. The proposed isogenic stratification
of the set of complex matrices bears similarities to the Schubert cell
stratification of a homogeneous algebraic manifold. An array of potential
applications to current investigations in computational matrix analysis is
briefly mentioned, touching concepts such as symmetric statistical models,
hierarchical matrices and coherent matrix organization induced by partition
trees.
