Some properties and applications of simple orthogonal matrices

A - Papers appearing in refereed journals

Constatine, A .G. and Gower, J. C. 1978. Some properties and applications of simple orthogonal matrices. IMA Journal of Applied Mathematics. 21 (4), pp. 445-454. https://doi.org/10.1093/imamat/21.4.445

AuthorsConstatine, A .G. and Gower, J. C.
Abstract

Conditions are found for a general transformation in the plane of two vectors u and v to be orthogonal. The results characterize a rotation in the (u, v)-plane by the angle ø between u and v and the angle of rotation. When ø = π/2 the Jacobi rotation matrix is a special case, but other choices of ø are interesting. The rotation that maps a single vector x into a vector y of the same size, by rotating in the (x, y)-plane, is found and this may be used in much the same way that Householder transforms are used. If (x1, y1) and (x2, y2) are pairs of vectors compatible in size and angle, the orthogonal matrix that rotates in a suitably chosen plane so that x1 → x2 and y1 → y2 is found. This has applications in mapping two columns of a matrix to a simple form, similar to Householder operations on a single column.
RESP-7948 and RESP-7741

Year of Publication1978
JournalIMA Journal of Applied Mathematics
Journal citation21 (4), pp. 445-454
Digital Object Identifier (DOI)https://doi.org/10.1093/imamat/21.4.445
Open accessPublished as non-open access
Output statusPublished
PublisherOxford University Press (OUP)
ISSN0272-4960

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