Generalized Eigenvalues of \$P_i^TLP_j+zP_i^TP_j\$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T10:00:12Z http://mathoverflow.net/feeds/question/57219 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/57219/generalized-eigenvalues-of-p-itlp-jzp-itp-j Generalized Eigenvalues of \$P_i^TLP_j+zP_i^TP_j\$ dan 2011-03-03T08:07:14Z 2011-03-03T08:07:14Z <p>I have the following generalized eigenvalue problem</p> <p>\$\det[P_i^TLP_j+zP_i^TP_j] = 0\$</p> <p>\$L\$ is a positive-semidefinite matrix with 1 eigenvalue at 0. More precisely, it is the combinatorial Laplacian matrix for a connected graph. \$P_i\$ (\$P_j\$) is the identity matrix with the i-th (j-th) column removed.</p> <p>What, if anything, can be said about the generalized eigenvalues \$z\$ of this problem?</p>