Schur Decomposition

In linear algebra, the Schur decomposition, or Schur triangulation, named after Issai Schur, is a matrix decomposition that expresses any complex square matrix as unitarily similar to an upper triangular matrix. The diagonal entries of that upper triangular matrix are exactly the eigenvalues of the original matrix, so the decomposition makes the full spectrum of a matrix visible directly on its diagonal. The Schur decomposition underlies many numerically stable algorithms for computing eigenvalues, since triangular matrices are far easier to work with than general ones.