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 …

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 …

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 …

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 …

Nov 15, 2017 · Is there any intuitive relation or theorem between 'invertible' and 'diagonalizable'? Not directly, in the sense that one would imply another. You can have matrices in all four …

Diagonalizable transformation restricted to an invariant subspace is diagonalizable Ask Question Asked 14 years, 3 months ago Modified 9 months ago

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 …

Note that the reason why $A$ is not diagonalizable is simple: both eigenvalues are $1$, thus if $A$ is diagonalizable, $D=I$ and thus $A=PDP^ {-1}=I$ contradiction.

Dec 21, 2017 · 6 All normal matrices are diagonalizable. Not all diagonalizable matrices are normal. Try to find an example of a diagonalizable but not normal matrix on your own (say, in 3 …