dc.contributor.author Stewart, G. W. en_US dc.date.accessioned 2004-05-31T22:49:34Z dc.date.available 2004-05-31T22:49:34Z dc.date.created 1998-01 en_US dc.date.issued 1998-10-15 en_US dc.identifier.uri http://hdl.handle.net/1903/934 dc.description.abstract The adjoint $A\adj$ of a matrix $A$ is the transpose of the matrix of the cofactors of the elements of $A$. The computation of the adjoint from its definition involves the computation of $n^{2}$ determinants of order $(n-1)$\,---\,a prohibitively expensive $O(n^{4})$ process. On the other had the computation from the formula $A\adj = \det(A)A\inv$ breaks down when $A$ is singular and is potentially unstable when $A$ is ill-conditioned. In this paper we first show that the ajdoint can be perfectly conditioned, even when $A$ is ill-conditioned. We then show that if due care is taken the adjoint can be accurately computed from the inverse, even when the latter has been inaccurately computed. In an appendix to this paper we establish a folk result on the accuracy of computed inverses. \end{minipage} \end{center} Also cross-referenced as UMIACS-TR-98-02 en_US dc.format.extent 164081 bytes dc.format.mimetype application/postscript dc.language.iso en_US dc.relation.ispartofseries UM Computer Science Department; CS-TR-3864 en_US dc.relation.ispartofseries UMIACS; UMIACS-TR-98-02 en_US dc.title On the Adjoint Matrix en_US dc.type Technical Report en_US dc.relation.isAvailableAt Digital Repository at the University of Maryland en_US dc.relation.isAvailableAt University of Maryland (College Park, Md.) en_US dc.relation.isAvailableAt Tech Reports in Computer Science and Engineering en_US dc.relation.isAvailableAt UMIACS Technical Reports en_US
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8280779123306274, "perplexity": 3325.156677272655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178351374.10/warc/CC-MAIN-20210225153633-20210225183633-00369.warc.gz"}