# Calculus: Compute a Schur Factorization of the Matrix

**Compute a Schur Factorization of the matrix A = **

Because A(1, 1) = (1,1), we know that (1,1) is an eigenvector of A.
By normalizing this eigenvector, we get U1 = (1/sqrt(2))(1,1)
From U1, we get U2 = vector perpendicular to U1 = (1/sqrt(2))(-1,1)
Q = (U1, U2) =
1/sqrt(2) | -1/sqrt(2) |

1/sqrt(2) | 1/sqrt(2) |

and Q^-1 =
1/sqrt(2) | 1/sqrt(2) |

-1/sqrt(2) | 1/sqrt(2) |

**Solution: T = (Q^-1)AQ is a Schur Factorization of A**
**T = **
**Q = **
1/sqrt(2) | -1/sqrt(2) |

1/sqrt(2) | 1/sqrt(2) |