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Schur Factorization
 Syntax B` = schur(`X`)` `[`U`, `B`] = schur(`X`)` See Also eigen , svd , qred , lu

Description
Computes a schur factorization of the matrix square matrix x, where X is real, double-precision, or complex. A schur factorization of X is a pair of matrices U and B such that ```      X = U B conj(U)' ```where U is a unitary matrix , the matrix B is in Schur form, and `conj(U)'` denotes the complex conjugate transpose of U. ``` ```The return values B and U have the same type and dimension as the matrix X. Note that because U is a unitary matrix, the matrices X and B have the same eigenvalues.

Real Schur Form
A real or double-precision matrix is in schur form if it is block diagonal with each diagonal block either a `1 x 1` or `2 x 2` matrix. In addition each of the `2 x 2` blocks has the form ```      / a  b \      \ c  a / ```where `b c < 0`. The eigenvalues corresponding to such a block is ```         +   -----      a  - \/ b c ```The eigenvalues corresponding to a `1 x 1` blocks is the value on the diagonal.

Complex Schur Form
A complex matrix is in schur form if it is upper triangular with its eigenvalues on the diagonal of the matrix.

Example
You can compute a schur factorization of the matrix ```      / 2 1 \      \ 1 2 / ```by entering ```      X = {[2., 1.], [1., 2.]}      [U, B] = schur(X)      print B ``` which returns ```      {      [ 3 , 0 ]      [ 0 , 1 ]      } ``` If you continue this example by entering ```      U * B * U' ``` O-Matrix will respond ```      {      [ 2 , 1 ]      [ 1 , 2 ]      } ``` (Note that because `X` is not complex, `U` is not complex and it is not necessary to take the complex conjugate of `U` in the example above.)