Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.

The Hermitian matrix A could be represented as A=Q·T·Q ^H, where Q is an unitary matrix, and T is a real tridiagonal matrix. We can say that matrix A is reduced to a tridiagonal matrix via a similarity transformation: Q ^H·A·Q = T.

As a result of HMatrixTD subroutine, matrix A is replaced by the tridiagonal matrix T and a sequence of reflections transformations stored in a compact form. The format of the matrix and the subroutine parameters are described in detail in the subroutine comments; there we can note an analogy with QR-decomposition, that uses the lower triangular part of the matrix R to store the matrix Q and utilizes a very similar data storage format. As with QR decomposition, a subroutine for "unpacking" the matrix Q is presented: HMatrixTDUnpackQ.

This algorithm is transferred from the LAPACK library.

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