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

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## Abstract

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.
Original language English 517-525 8 SIAM Journal on Matrix Analysis and Applications 35 24 Apr 2014 https://doi.org/10.1137/130920897 E-pub ahead of print - 24 Apr 2014

## Keywords

• block triangluar preconditioner
• convergence
• eigenvalues
• eigenvectors
• iterative method
• saddle point system