# On the eigenvalues and eigenvectors of block triangular preconditioned block matrices

Pestana, Jennifer (2014) On the eigenvalues and eigenvectors of block triangular preconditioned block matrices. SIAM Journal on Matrix Analysis and Applications, 35. pp. 517-525. ISSN 0895-4798

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.