Let A = 3 2 2 2 3 -2 (a) Find the eigenvalues and a set...

•  
• 
  

Transcribed Image Text:

Let A = 3 2 2 2 3 -2 (a) Find the eigenvalues and a set of orthonormal eigenvectors for ATA (you may use a computer to simplify and solve the characteristic polynomial). These are the right singular vectors. (b) For each eigenvector v in (a) which is not associated with a zero eigenvalue, compute Av and normalize it so that it has length 1. These are the left singular vectors. (c) Find the eigenvalues and a set of orthonormal eigenvectors for AAT. Check that these are the same (up to sign) as the left singular vectors. (d) Find the singular values 01, 02 of A. (e) Write down the matrices U, Σ and V in the SVD of A and check that A = UEVT (you can use a computer to do the calculations and just write down that you checked it). Let A = 3 2 2 2 3 -2 (a) Find the eigenvalues and a set of orthonormal eigenvectors for ATA (you may use a computer to simplify and solve the characteristic polynomial). These are the right singular vectors. (b) For each eigenvector v in (a) which is not associated with a zero eigenvalue, compute Av and normalize it so that it has length 1. These are the left singular vectors. (c) Find the eigenvalues and a set of orthonormal eigenvectors for AAT. Check that these are the same (up to sign) as the left singular vectors. (d) Find the singular values 01, 02 of A. (e) Write down the matrices U, Σ and V in the SVD of A and check that A = UEVT (you can use a computer to do the calculations and just write down that you checked it).