China
Africa
Explore chapters and articles related to this topic
Orthogonality
Published in Qingwen Hu, Concise Introduction to Linear Algebra, 2017
12. Let A=1-10110011 $ A = \left[ {\begin{array}{*{20}l} 1 \hfill & { - 1} \hfill & 0 \hfill \\ 1 \hfill & 1 \hfill & 0 \hfill \\ 0 \hfill & 1 \hfill & 1 \hfill \\ \end{array} } \right] $ . Use the Householder transformation to find an orthogonal matrix Q such that QTA is upper triangular.
H
Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
Hotelling transform a transformation whose basis vectors are the eigenvectors of the covariance matrix of the random vectors. See Karhunen-Lo` ve transformation. e Hough transform a transform which transforms image features and presents them in a suitable form as votes in a parameter space, which may then be analyzed to locate peaks and thereby infer the presence of desired arrangements of features in the original image space: typically, Hough transforms are used to locate specific types of object or shape in the original image. Hough transform detection schemes are especially robust. Householder transformation a matrix Q that maps each vector to its reflection through a defined hyperplane; specifically, uu T uT u reflects through the plane having normal vector u. Q = I -2
Linear Vector Spaces
Published in Sohail A. Dianat, Eli S. Saber, ®, 2017
Sohail A. Dianat, Eli S. Saber
QR factorization factors a rectangular matrix into the product of a unitary and an upper triangular matrix. An important application of QR factorization is solving linear systems of equations. This is due to the fact that the inverse of unitary matrices is obtained from the conjugate transpose (Hermitian operation). It is also a useful tool in solving least squares problems. Different techniques, such as Householder transformation and Gram–Schmidt decomposition, are used for QR factorization.
Numerical Simulation of Unsteady Channel Flow with a Moving Indentation Using Solution Dependent Weighted Least Squares Based Gradients Calculations over Unstructured Mesh
Published in Heat Transfer Engineering, 2021
Chandrakant R. Sonawane, Yogesh B. More, Anand Kumar Pandey
Bischof et al. [33] had introduced Lapack routine DGELS is used to solve the equivalent least-squares problem. This routine uses the Householder transformation for the QR method to solve the full rank least-squares problem.