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NBEIGVAL

Purpose:

Computes the Eigenvalues of a square table without a preliminary balancing step.

Syntax:

NBEIGVAL(a)

Returns:

A series with as many rows as the input table. Each entry in the series is an Eigenvalue. The Eigenvalue in row n of NBEIGVAL corresponds to the Eigenvector in column n of NBEIGVEC .

Example:

W1: {{8i,    0, 1+i},

     { 0, 1001,  3i}, 

     {90,    i, 200}} 

nbeigval(W1) == {{  -0.43153 + 7.5348i},

                 { 200.44    + 0.46525i}, 

                 {1001.0     - 0.0i}} 

Remarks:

EIGVAL and EIGVEC first perform a balancing step in which the rows and columns are transformed to have root mean squares as close as possible while leaving the Eigenvalues and Eigenvectors unchanged. In most cases, this improves the accuracy of EIGVAL and EIGVEC, but in some cases it does not. BALANCE can be used to check that relatively small table elements have not become unduly magnified by the balancing step. If they have, then NBEIGVAL and NBEIGVEC are likely to yield better results.

See Also:

BALANCE

EIG

EIGVAL

EIGVEC

NBEIGVEC