Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there a general solution to the following matrix equation.

$A - BAB^T = C$
where B is known but can be any non-symmetric square matrix, C is known and invertible, all are n by n matrices. Is there a solution to A? or we need to use numerical methods?

share|cite|improve this question
up vote 0 down vote accepted

This is a discrete Lyapunov equation, and stable, accurate numerical methods exist to solve it (for certain conditions on $C$).

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.
{"cc_re__cc_re__cc_by_sa_3_0": ["                    <li><a href=\"//area51.stackexchange.com\" title=\"proposing new sites in the Stack Exchange network\">Area 51</a></li>\r\n                        <li><a href=\"//careers.stackoverflow.com\">Stack Overflow Careers</a></li>\r\n                    \r\n                </ol>\r\n            </td>\r\n    </tr>\r\n</table>\r\n                </div>\r\n            </div>\r\n            <div id=\"copyright\">\r\n                site design / logo &#169; 2016 Stack Exchange Inc; user contributions licensed under <a href=\"https://creativecommons.org/licenses/by-sa/3.0/\" rel=\"license\">cc by-sa 3.0</a> \r\n                with <a href=\"http://blog.stackoverflow.com/2009/06/attribution-required/\" rel=\"license\">attribution required</a>\r\n            </div>\r\n            <div id=\"svnrev\">\r\n                rev 2016.5.27.3620\r\n            </div>\r\n        </div>\r\n    </div>\r\n    <noscript>\r\n        <div id=\"noscript-warning\">Mathematics Stack Exchange works best with JavaScript enabled<img src=\"http://pixel.quantserve.com/pixel/p-c1rF4kxgLUzNc.gif\" alt=\"\" class=\"dno\"></div>\r\n    </noscr"], "copyright__copyright__copyright": ["e n by n matrices. Is there a solution to A? or we need to use numerical methods?\n\nshare|cite|improve this question\nup vote 0 down vote accepted\n\nThis is a discrete Lyapunov equation, and stable, accurate numerical methods exist to solve it (for certain conditions on $C$).\n\nshare|cite|improve this answer\n\nYour Answer\n\n\u00a0\ndiscard\n\nBy posting your answer, you agree to the privacy policy and terms of service.\n\nNot the answer you're looking for? Browse other questions tagged or ask your own question."]}