1. ## Singular value decomposition

Suppose $\displaystyle A$ is a 2 by 2 symmetric matrix with unit eigenvectors $\displaystyle u_1$ and $\displaystyle u_2$. If its eigenvalues are 3 and -2, what are the matrices $\displaystyle U$, $\displaystyle \sum$, $\displaystyle V'$ in its SVD?

($\displaystyle V'$ is the transpose of $\displaystyle V$.)

2. Hint

The eigenvalues of A^hA are 9 and 4 so, the singular values of A are 3 and 2 .

3. Originally Posted by FernandoRevilla
Hint

The eigenvalues of A^hA are 9 and 4 so, the singular values of A are 3 and 2 .
Thanks. So I get:

Is that right?

4. Originally Posted by alexmahone
Is that right?

Using the standard method, the factorization is

[ u_1, -u_2 ]^t A [ u_1, u_2 ] = diag [ 3, 2 ]

5. Originally Posted by FernandoRevilla
Using the standard method, the factorization is

[ u_1, -u_2 ]^t A [ u_1, u_2 ] = diag [ 3, 2 ]
Are you saying that my answer in post #3 is wrong? (Sorry for being so slow; I'm self studying Linear Algebra from Strang and he isn't very clear most of the time.)

6. Originally Posted by alexmahone
Are you saying that my answer in post #3 is wrong? (Sorry for being so slow; I'm self studying Linear Algebra from Strang and he isn't very clear most of the time.)

Your answer is right. I also provided the matrix U , that is

V = [ u_1, - u_2] , U = [ u_1 , u_2 ]