High Quality Content by WIKIPEDIA articles! In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is an important matrix decomposition. A constructive proof for the Schur decomposition is as follows: every operator A on a complex finite-dimensional vector space has an eigenvalue , corresponding to some eigenspace V . Let V be its orthogonal complement. It is clear that, with respect to this orthogonal decomposition, A has matrix representation (one can pick here any orthonormal bases spanning V and V respectively) A = begin{bmatrix} lambda , I_{lambda}

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