Quick way to check if a matrix is diagonalizable.
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 distinct …
Is there any relationship between 'invertible' and 'diagonalizable'?
Nov 15, 2017 · There are invertible matrices which are not diagonalizable and there are diagonalizable matrices which are not invertible. There are matrices which are neither diagonalizable nor invertible.
Diagonalisability of 2×2 matrices with repeated eigenvalues
May 15, 2017 · As the other posters comment, there are diagonal matrices which are not multiples of the identity, for example $$ \begin {bmatrix}1&0\\0&2\end {bmatrix} $$ and if all the eigenvalues of a …
Diagonalizable matrices with complex values are dense in set of $n ...
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 $\mathbb {R}^ {n^2}$.
linear algebra - Sufficient condition for a matrix to be diagonalizable ...
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 form when the …
linear algebra - What kind of matrices are non-diagonalizable ...
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 lose all the …
Are matrices always diagonalizable in the complex field?
Oct 13, 2022 · No, not every matrix over $\Bbb C$ is diagonalizable. Indeed, the standard example $\begin {pmatrix} 0&1\\0&0 \end {pmatrix}$ remains non-diagonalizable over the complex numbers.
A matrix is diagonalizable, so what? - Mathematics Stack Exchange
I mean, you can say it's similar to a diagonal matrix, it has n independent eigenvectors, etc., but what's the big deal of having diagonalizability? Can I solidly perceive the differences between two linear …
Are positive definite matrices necessarily diagonalizable and when …
Many authors mean positive definite and symmetric (or self-adjoint) when they write simply positive definite. It is symmetry which implies diagonalizable, so really this is a question about what you mean …
Prove that simultaneously diagonalizable matrices commute
Regarding the second part of (b), since it can't be true as asked, we could modify it to a more interesting question: If two diagonalizable matrices commute, are they simultaneously diagonalizable?