f08ffc generates the real orthogonal matrix
, which was determined by
f08fec when reducing a symmetric matrix to tridiagonal form.
f08ffc is intended to be used after a call to
f08fec, which reduces a real symmetric matrix
to symmetric tridiagonal form
by an orthogonal similarity transformation:
.
f08fec represents the orthogonal matrix
as a product of
elementary reflectors.
The computed matrix
differs from an exactly orthogonal matrix by a matrix
such that
where
is the
machine precision.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The complex analogue of this function is
f08ftc.
This example computes all the eigenvalues and eigenvectors of the matrix
, where
Here
is symmetric and must first be reduced to tridiagonal form by
f08fec. The program then calls
f08ffc to form
, and passes this matrix to
f08jec which computes the eigenvalues and eigenvectors of
.