See how to diagonalize a matrix along with examples of matrix diagonalization. Understand when a matrix is diagonalizable and its relation to eigenvalues.

Jun 4, 2016 · @MahNeh A $2\times2$ matrix with coincident eigenvalues is diagonalizable if and only if it is diagonal. Anyway, the eigenspace relative to the unique eigenvalue $1$ has …

Jul 26, 2018 · When a matrix is diagonalizable, of course, by definition the diagonal form is similar to the original matrix. Note that similarity holds, more in general, also with the Jordan normal …

Jul 8, 2015 · In short, diagonalizable of a matrix means that the matrix has independent set of eigenvectors that can span the entire space. There are several ways to decide whether matrix …

Dec 5, 2018 · If questions (a) and (b) are resolved, I can see how this would imply (c), but why is this claim true? Here is another approach to this problem, but this one seems to be more …

Apr 16, 2012 · A matrix is diagonalizable if and only if the algebraic multiplicity equals the geometric multiplicity of each eigenvalues. By your computations, the eigenspace of …

Apr 12, 2016 · ^I edited it to fix that. To the OP, do you know how to prove that a normal matrix is diagonalizable? If so, orthogonal matrices are normal, which would finish the proof.

Nov 6, 2016 · A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is equal to the multiplicity of the eigenvalue. Meaning, if you find matrices with …

4 I'll try an answer in a different (equivalent) direction: what happens when the matrix is not diagonalizable? First of all, this must mean that some of the matrix's eigenvalues occur more …

But, there are non-diagonalizable matrices that aren't rotations - all non-zero nilpotent matrices. My intuitive view of nilpotent matrices is that they ''gradually collapse all dimensions/gradually …