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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 m ×n matrix A,
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