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 than …

Suppose $A$ is an $m \\times m$ matrix which satisfies $A^{n}=1$ for some $n$, then why is $A$ necessarily diagonalizable. Not sure if this is helpful, but here's my ...

Yes, it is possible for a matrix to be diagonalizable and to have only one eigenvalue; as you suggested, the identity matrix is proof of that. But if you know nothing else about the matrix, you cannot …

Sep 2, 2024 · 15 I'm trying to go about the proof that any matrix that is nilpotent (i.e. $\exists N \in\Bbb N. A^N = \mathbf {0}$) cannot be diagonalizable. I believe that the best way to go about this is by …

Diagonalizable matrices with complex values are dense in set of $n \times n$ complex matrices. He defined a metric (I believe) that was somehow related to the usual metric on $\mathbb {R}^ {n^2}$.

Jan 29, 2024 · This question is from an older exam of Linear Algebra of my university, it's one of 14 questions of the exam. They want to know which of these matrices are diagonalizable. The problem …

In symmetric matrix geometric multiplicity to be equal to the algebraic multiplicity of eigenvalues.Hence we are heaving complete set of the eigen vectors and Eigenvectors of the symmetric can always be …

I am currently self-learning about the matrix exponential and found that determining the matrix of a diagonalizable matrix is pretty straight forward :). I do not, however, know how to find the exponential …

Minimal polynomial and diagonalizable matrix Ask Question Asked 14 years, 4 months ago Modified 14 years, 4 months ago

Moreover, every real symmetric matrix is diagonalizable, whether or not its eigenvalues are distinct.