Is there a way to relate Eigenvalues to the column space and nullspace of a matrix?
I believe a matrices with different eigenvalues would have a different column spaces and/or nullspace. Is this correct?
I am wondering if you can prove that the Eigenvalues of A and A^T are equal using properties of column spaces and nullspaces.
My thinking is: If you transform a matrix A into B, if the row space of B is orthogonal to the nullspace of A, and the column space of B is orthogonal to the left nullspace of A, then matrices A and B have the same eigenvalues.