Name
Title | ||
|---|---|---|
Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations |
Abstract | ||
|---|---|---|
We present a practical and efficient means to compute the singular value decomposition (SVD) of a real or complex quaternion matrix A based on bidiagonalization of A to a real or complex bidiagonal matrix B using quaternionic Householder transformations. Computation of the SVD of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from the product of the Householder transformations and the real or complex singular vectors of B. We show in the paper that left and right quaternionic Householder transformations are different because of the non-commutative multiplication of quaternions and we present formulae for computing the Householder vector and matrix in each case. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.amc.2006.04.032 | Applied Mathematics and Computation |
Keywords | Field | DocType |
complex quaternion,complex matrix,quaternion singular value decomposition,singular value decomposition,present formula,quaternionic householder transformation,complex quaternion matrix,quaternion householder transformation,quaternion,householder transformation,householder vector,diagonalization,complex singular vector,singular vector,singular value,complex bidiagonal matrix b,numerical analysis | Singular value decomposition,Singular value,Algebra,Quaternion,Bidiagonal matrix,Householder's method,Bidiagonalization,Householder transformation,Mathematics,QR decomposition | Journal |
Volume | Issue | ISSN |
182 | 1 | Applied Mathematics and Computation |
Citations | PageRank | References |
10 | 1.28 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stephen J. Sangwine | 1 | 130 | 19.63 |
| Nicolas Le Bihan | 2 | 254 | 23.35 |