# NBEIGVEC

## Purpose:

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

## Syntax:

NBEIGVEC(a)

## Returns:

A square table of the same dimensions
as the input table. Each column of the output table is an Eigenvector.
The Eigenvector in column n of NBEIGVEC corresponds to the Eigenvalue
in row n of NBEIGVAL .

## Example:

W1: {{8i, 0,
1+i},

{
0, 1001, 0+3i},

{90,
0+i, 200}}

nbeigvec(W1) ==

{{-0.911 + 0.048i, -0.006 – 0.005i, 0.000
– 0.000i},

{
0.000 – 0.001i, 0.000
+ 0.004i, -1.000 – 0.005i},

{
0.409 – 0.006i, -1.090 + 0.096i, 0.000
– 0.001i}}

## 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

NBEIGVAL