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Suppose I have a matrix [itex] A_{N\times N}[/itex]. I compute its eigenmodes

[itex] A V = V \Lambda[/itex].

[itex] V, \Lambda[/itex] are eigenvectors and eigenvalues of size [itex] N\times N [/itex]. The eigenvalues are descending.

Now I cut off several eigenmodes (the ones having small value), it becomes

[itex] A V_{N \times n} = V_{N \times n} \Lambda_{n \times n}[/itex].

What I want is to reconstruct [itex]A[/itex] from [itex] V_{N \times n}, \Lambda_{n \times n}[/itex].

It seems that in Matlab, if I just modify the above equation

[itex] A = V_{N \times n} \Lambda_{n \times n}V^{-1}_{N \times n}[/itex],

it will not work.

So my question is: how can I reliably reconstruct the original matrix by using its reduced eigenmodes? Thanks!!

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# Reconstruct A from its reduced eigenparis

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