User marjeta - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T20:45:28Z http://mathoverflow.net/feeds/user/30376 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eigenvalues-elementary-proof real symmetric matrix has real eigenvalues - elementary proof marjeta 2013-01-11T13:22:17Z 2013-02-28T14:21:46Z <p>Every real symmetric matrix has at least one real eigenvalue. Does anyone know how to prove this elementary, that is without the notion of complex numbers?</p> http://mathoverflow.net/questions/48908/is-the-invariant-subspace-problem-interesting/120292#120292 Comment by marjeta marjeta 2013-02-06T10:50:05Z 2013-02-06T10:50:05Z not yet... <a href="http://cafematematico.com/2013/02/05/statement-from-cowen-and-gallardo/" rel="nofollow">cafematematico.com/2013/02/05/&hellip;</a> http://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eigenvalues-elementary-proof Comment by marjeta marjeta 2013-01-13T21:01:51Z 2013-01-13T21:01:51Z @Tom, Gerald: I apologize for being unclear. I've now corrected my question (I haven't done that before since I thought editing already posted questions could also be confusing). http://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eigenvalues-elementary-proof Comment by marjeta marjeta 2013-01-11T23:24:21Z 2013-01-11T23:24:21Z To clarify the situation - if a real symmetric matrix has one real eigenvalue, all its eigenvalues are real (which can be proved by induction)! http://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eigenvalues-elementary-proof Comment by marjeta marjeta 2013-01-11T13:49:52Z 2013-01-11T13:49:52Z Indeed the question was posed for pedagogical purposes, elementary meaning that a first-year engineering student would be able to follow it!