f08ftc generates the complex unitary matrix
, which was determined by
f08fsc when reducing a Hermitian matrix to tridiagonal form.
f08ftc is intended to be used after a call to
f08fsc, which reduces a complex Hermitian matrix
to real symmetric tridiagonal form
by a unitary similarity transformation:
.
f08fsc represents the unitary matrix
as a product of
elementary reflectors.
The computed matrix
differs from an exactly unitary matrix by a matrix
such that
where
is the
machine precision.
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 real analogue of this function is
f08ffc.
This example computes all the eigenvalues and eigenvectors of the matrix
, where
Here
is Hermitian and must first be reduced to tridiagonal form by
f08fsc. The program then calls
f08ftc to form
, and passes this matrix to
f08jsc which computes the eigenvalues and eigenvectors of
.