diagonalisation

A brief description of the well known Joint Approximation Diagonalisation of Eigenmatrices (JADE) algorithm and Generalized Eigenvalue Decomposition (GED) algorithm is presented.

Detailed information regarding the structure each of the deformed HF sp orbits, their energies, and the parentage of each of the HF intrinsic state in the [[PHI].sup.J] states (e.g., the linear combination of [[phi].sup.J.sub.MK] obtained in the band mixing diagonalisation) can be obtained from the authors.

The source separation beamformer matrix T, in the whitened domain constraint, will be found by an iterative process of joint diagonalisation such that the solutions of the beamformer columns elements are scaled to unit-norm vectors ([parallel][t.sub.i][parallel]) as a decorrelation step defined by the properties of the constant modulus algorithm in the presence of noise [12].

Conjugation arises as a broader concept than that of principal directions (a particular case, where [[bar.[GAMMA]].sub.v] is collinear with V), but keeping the algebraic property of diagonalisation of tensors, if expressed in covariant components.

Both matrices (4a) and (4b) have the same, frequency-dependent couple of double-multiplicity degenerate eigenvalues, but due to the structure of matrices F and R, diagonalisation can indeed be achieved in a frequency-independent way.

Owen, "A joint diagonalisation approach for linear stochastic systems," Computers and Structures, vol.

(18) Three pairs of eigenvalues [[lambda].sub.1], [[lambda].sub.2], [[lambda].sub.3]) and eigenvectors ([[epsilon].sub.1], [[epsilon].sub.2], [[epsilon].sub.3]) can be obtained by diagonalisation of the tensor matrix.