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**HOMOGEN(***matrix***)**

where *matrix* is a numeric matrix or literal.

The HOMOGEN function solves the homogeneous system of
linear equations **A*****X** = **0** for **X**.
For at least one solution vector **X**
to exist, the *m* ×*n* matrix **A**,
, has to be of rank *r* < *n*.
The HOMOGEN function computes an *n* ×(*n*-*r*)
column orthonormal matrix **X** with the property
**A*****X** = **0**, **X**' **X** = **I**.
If **A**'**A** is ill conditioned, rounding-error
problems can occur in determining the correct rank of **A**
and in determining the correct number of solutions **X**.
Consider the following example
(Wilkinson and Reinsch 1971, p. 149):

a={22 10 2 3 7, 14 7 10 0 8, -1 13 -1 -11 3, -3 -2 13 -2 4, 9 8 1 -2 4, 9 1 -7 5 -1, 2 -6 6 5 1, 4 5 0 -2 2}; x=homogen(a);These statements produce the solution

X 5 rows 2 cols (numeric) -0.419095 0 0.4405091 0.4185481 -0.052005 0.3487901 0.6760591 0.244153 0.4129773 -0.802217In addition, this function could be used to determine the rank of an

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