Householder transformations - PowerPoint PPT Presentation

Example:

Householder Transformations. Example:. DEF:. is called Householder matrix ( Reflection, Transformation). Householder Transformations. Example. DEF:. is called Householder matrix ( Reflection, Transformation). Rem :. They are rank-1 modifications of the identity.

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Scientific Computing

Scientific Computing. QR Factorization Part 1 – Orthogonal Matrices, Reflections and Rotations. Orthogonal Matrices. Matrix Factoring : So far, we have seen that we can factor a non-singular matrix A as A = LU, where L is lower triangular and U is upper triangular.

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Linear Least Squares

Linear Least Squares. Paul Heckbert Computer Science Department Carnegie Mellon University. Orthogonal and Hermitian Matrix. A square matrix Q is orthogonal iff Q -1 = Q T Q T Q = QQ T = I its rows are orthonormal  its columns are orthonormal

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