eigenvalue diagonalization in matlab

I need to calculate eigenvalue diagonalization of B = P-1VP by showing P-1, V and P. I couldn't find anything online and in eig function. Can someone help me solve this issue?

Answer 1

[Walter Roberson]

The typical semantics for eig is

[V, D] = eig(A)

which calculates A*V = V*D

If you pre-multiply by inv(V) then inv(V)*A*V = inv(V)*V*D which is inv(V)*A*V = D which has form that the user is looking for, if we rename some variables,

[P, B] = eig(V)

would then become inv(P)*V*P = B -- where V would be the input and B would be the diagonal output, and the whole thing would be confusing to people accustomed to V being an output and B (or other full matrix) being the input.

What if we post-multiply?

A*V*inv(V) = V*D*inv(V)

then A = V*D*inv(V) . But this is the wrong form, having an original matrix on the left and its inverse on the right. We would need to do something like

[invP, V] = eig(B);
P = inv(P);

and that would satisfy -- at the expense, again, of confusion from people who are accustomed to V being the role of the full matrix, not of the diagonal.

Possible? Yes, with some confusion. Not recommended, however.

Answer 2

[Paul]

Does eig not provide the solution, assuming a solution exists?