New posts in Linear Transformations

If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable

If $f(x)=ax+b$ is linear, why is $f(\gamma x) \neq \gamma f(x)$

Is every eigenvector of AA an eigenvector of A?

Is my understanding of matrices correct?

There does not exist a onto ring homomorphism from $M_{n+1 \times n+1}(\mathbb F) \to M_{n \times n}(\mathbb F) $ for any field $\mathbb F.$

What is the difference between codomain and range?

Orbits of vectors under the action of $\mathrm{GL}_n(\mathbb Q)$

Why is the eigenvalue equation $ Ax = \lambda x $ nonlinear?

Intuitively, $why$ do defective matrices have extra eigenvalues?

How to show that $f:V\to V$ is linear?