For the 3×2 matrix A: a) Determine the eigenvalues of ATA, and confirm that your eigenvalues...

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Question

For the 3×2 matrix A:

101

a) Determine the eigenvalues of A^TA, and confirm that your eigenvalues are consistent with the trace and determinant of A^TA.

b) Find an eigenvector for each eigenvalue of A^TA.

c) Find an invertible matrix P and a diagonal matrix D such that P^-1(A^TA)P = D.

d) Find the singular value decomposition of the matrix A; that is, find matrices U, Σ, and V such that A = UΣV^T.

e) What is the best rank 1 matrix that approximates A?

Answer 1

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