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 …

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 …

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 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 …

For the second matrix, the algebraic multiplicity and the geometric multiplicity of both lambdas are equal, so this is diagonalizable according to my textbook. But there are still only two distinct …

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 …