Re: Command to obtain a matrix from its eigenvalues

"Bruno Luong" <b.luong@xxxxxxxxxxxxxxxxxxxx> wrote in message <h03in6$lro$1@xxxxxxxxxxxxxxxxxx>...

From what I have learn - I disagree: matrix A has only *one* eigenvalue {1}, since the kernel (nullspace) of [A-1*eye(2)] is one dimension space.

So A does *not* have {1,1} as eigenvalues. It has {1} as eigenvalue.


Well...... I've seen a number of linear algebra texts in which repeated eigenvalues are not considered to be single eigenvalues. They are considered to have "multiplicity" n>1.

But even we accept your framework for a moment, it doesn't simplify the problem. Even if the eigenvalue set is is just {1}, I've still presented you with an example of a real matrix A which is not representable as P*diag(Eigenvalues)*inv(P). Since diag{1}=1, the latter just reduces to

P*diag(Eigenvalues)*inv(P) = I ~=A

It also makes the OP's inverse problem more difficult. If you start with the case where the eigenvalue set is {1} and you don't know its multiplicity, you can't know what the size of the original matrix is...
.

Relevant Pages

  • Re: Powering a matrix?
    ... finding the Jordan form can be a pain. ... the and a Jordan block corresponds to ... suppose M has two different eigenvalues r of multiplicity ...
    (sci.math)
  • Re: Definition of singular values of an operator
    ... the same multiplicity, of course). ... for any square matrices A and B, the eigenvalues ... See e.g. the thread "Linear algebra" from July 2004 ...
    (sci.math)
  • Re: Are eigenvectors independent
    ... Say a matrix A has 5 eigenvalues (where one of them as multiplicity 2 ... as a root of characteristic equation of A). ... Then 1 is a root of the characteristic polynomial with multiplicity 2, ...
    (sci.math)
  • MuPAD: eigenvalue extraction from a list of sub-lists
    ... I am trying to extract the eigenvalues, ... multiplicity from the list of sub-lists generated by the ...
    (comp.soft-sys.matlab)
  • Re: eigenvalues of powers of a matrix
    ... multiplicity, so r <= n). ... Let k be a positive integer. ... Conjecture: All of the eigenvalues of A^k are in the set ... Then the set of eigenvalues of A is ...
    (sci.math)