Let A=
[7 -4 4]
[-4 5 0]
[4 0 9]
a) Orthogonally diagonalize A
b) Use answer from a) to construct a spectral decomposition for A.
c) Suppose that x=[1 2 1] and let u be the eigen vector from a) corresponding to the largest eigen-value of A. If W=Span {u}, then use b) to decompose x into a sum of vectors, one in W and the other in W¡Í.
2 answers