An elementrary reflector is a vector that implements reflection (mathematics). It is also referred to as a triangular factor, and is a triangular matrix. Elementary reflectors are used in the Householder transformation. IT IS KNOWN AS MARK a lunitice insain int gw brain ... In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix where the entries below or above the main diagonal are zero. ... In mathematics, a Householder transformation in 3-dimensional space is the reflection of a vector in a plane. ...
The routines in LAPACK "*LARZ" apply an "elementary reflector" H to a M-by-N Matrix, from either the left or the right. The elementary reflector is expressed as Linear Algebra PACKage (LAPACK). ... Look up Matrix in Wiktionary, the free dictionary The word matrix (plural matrices, or less often, matrixes) has several meanings. ...
H = I − τ v· v′
where τ is a scalar and v is a vector. H is a product of k elementary reflectors.
A block reflector is formed out of k elementary reflectors by the routines "*LARZT", which forms the triangular factor T of a block reflector H of order > n. A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one. ...
LAPACK routines
"*larf" applies an elementary reflector to a general rectangular matrix.
"*larfc" applies the conjugate transpose of an "elementary reflector" to a general matrix.
"*larfg" generates an elementary reflector Householder matrix.
"*larzc" applies (multiplies by) the conjugate transpose of an elementary reflector as returned by "*tzrzf" to a general matrix.
"*larz" applies an elementary reflector as returned by "*tzrzf" to a general matrix.
Feeds |
Contact