Denman, Eugene D.2022-09-192022-09-191973197313806105https://hdl.handle.net/10657/11397A 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.application/pdfenThis 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.Thesisreformatted digital