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 …

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 …

Nov 21, 2023 · Learn all about matrix diagonalization with our short video lesson. Watch now to learn about its intricate process and see examples, followed by an optional quiz.

The fact that a hermitian matrix is diagonalizable is a corollary of the theorem about normal matrices.

A matrix is diagonalizable if and only if the algebraic multiplicity equals the geometric multiplicity of each eigenvalues. By your computations, the eigenspace of $\lambda=1$ has dimension $1$; …

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 …

Diagonalizable transformation restricted to an invariant subspace is diagonalizable Ask Question Asked 13 years, 11 months ago Modified 5 months ago

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Dec 21, 2017 · 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 x 3 …