#### APPROXIMATE JOINT DIAGONALIZATION USING NONORTHOGONAL MATRICES

Arie Yeredor

Several Blind Source Separation algorithms require the
approximate joint diagonalization of a set of matrices.
Most existing algorithms for approximate joint diag
onalization are restricted to finding an orthogonal di
agonalizing matrix. It has therefore become common
practice to first find the nonorthogonal factor of the
diagonalizing matrix by prewhitening the data, and
then proceed to find the orthogonal factor using ex
isting algorithms. However, such an approach favors
exact diagonalization of one matrix (usually the data
correlation matrix), possibly at the expense of poor di
agonalization of the other matrices. In this paper we
propose a joint diagonalization algorithm which uses
general (not necessarily orthogonal) matrices. The use
of this algorithm enables to eliminate the traditional
''hard whitening'' phase, which is known to limit the
performance, especially under noisy conditions. We
demonstrate the improved performance via simulations
results.