# last column of SPD matrix given it's spectral decomposition

I'm working on this application where I get the spectral decomposition (O,D) of a matrix A for free (A is of full rank) but not A itself, and I need to only recover the last column of A. I was wondering if there was a more efficient way to do this than reconstructing the whole of A first?

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What is $D$? Diagonal matrix of eigenvalues? Do you have the eigenvector matrices for free too? –  Jesse Chan Mar 13 '14 at 17:53
@JLC: I edited the question to avoid confusion! Thanks for the hint –  user189035 Mar 13 '14 at 19:05