Hi all,

Suppose I have a matrix $\displaystyle A_{N\times N}$. I compute its eigenmodes

$\displaystyle A V = V \Lambda$.

$\displaystyle V, \Lambda$ are eigenvectors and eigenvalues of size $\displaystyle N\times N $. The eigenvalues are put in a descending order.

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

$\displaystyle A V_{N \times n} = V_{N \times n} \Lambda_{n \times n}$.

What I want is to reconstruct $\displaystyle A$ from $\displaystyle V_{N \times n}, \Lambda_{n \times n}$.

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

$\displaystyle A = V_{N \times n} \Lambda_{n \times n}V^{-1}_{N \times n}$,

it will not work.

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