What is the relationship between the upper triangular matrix and diagonal matrix in a operator? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-21T08:53:21Z http://mathoverflow.net/feeds/question/17705 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17705/what-is-the-relationship-between-the-upper-triangular-matrix-and-diagonal-matrix What is the relationship between the upper triangular matrix and diagonal matrix in a operator? Lee 2010-03-10T09:18:35Z 2010-03-10T09:18:35Z <p>In complex vector space, the characteristic polynomial of a operator has n roots. So the operator has n eigenvalues. Obviously, the operator has a upper triangular matrix. If n roots are distinct, the operatior will have a diagonal matrix. If there exists repeated roots, the operator should at least have a upper triangular matrix. What is the relationship between the upper triangular matrix and diagonal matrix in the operator? Could I say that a operator has a diagonal matrix if it has a upper triangular matrix?</p> <p>Thanks in advance</p>