A new similarity transformation method for eigenvalues and eigenvectors
dc.contributor.advisor | Denman, Eugene D. | |
dc.contributor.committeeMember | Ander, Willard N., Jr. | |
dc.contributor.committeeMember | Bargainer, James D., Jr. | |
dc.contributor.committeeMember | Sinkhorn, Richard D. | |
dc.contributor.committeeMember | Tavora, Carlos J. | |
dc.creator | Beavers, Alex Newsom, Jr. | |
dc.date.accessioned | 2022-09-19T20:43:01Z | |
dc.date.available | 2022-09-19T20:43:01Z | |
dc.date.copyright | 1973 | |
dc.date.issued | 1973 | |
dc.description.abstract | A new method of finding the eigenvalues and eigenvectors of an arbitrary complex matrix is presented. The new method is a similarity transformation method which transforms an arbitrary N x N matrix to a Jordan canonical form in N-l or less transformations. Each transformation matrix is a matrix function— the matrix sign function with a [plus-minus]1 added to the main diagonal elements. Using this matrix function as a similarity transformation gives a block diagonal form which is a reduced form of the transformed matrix. As the Jordan canonical form is found, the eigenvectors are simultaneously found since the product of transformation matrices must be a matrix of eigenvectors. The theoretical development of the new method and a computational scheme with examples are given. In the examples, the computational scheme is applied successfully to matrices, which have characteristics that cause problems for most numerical techniques. | |
dc.description.department | Electrical and Computer Engineering, Department of | |
dc.format.digitalOrigin | reformatted digital | |
dc.format.mimetype | application/pdf | |
dc.identifier.other | 13806105 | |
dc.identifier.uri | https://hdl.handle.net/10657/11397 | |
dc.language.iso | en | |
dc.rights | This item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder. | |
dc.title | A new similarity transformation method for eigenvalues and eigenvectors | |
dc.type.dcmi | Text | |
dc.type.genre | Thesis | |
dcterms.accessRights | The full text of this item is not available at this time because it contains documents that are presumed to be under copyright and are accessible only to users who have an active CougarNet ID. This item will continue to be made available through interlibrary loan. | |
thesis.degree.college | Cullen College of Engineering | |
thesis.degree.department | Electrical Engineering, Department of | |
thesis.degree.discipline | Electrical Engineering | |
thesis.degree.grantor | University of Houston | |
thesis.degree.level | Doctoral | |
thesis.degree.name | Doctor of Philosophy |
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