Calculus: Compute a Schur Factorization of the Matrix

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

-3	4
-6	7

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 = **

1	10
0	3

**Q = **

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