Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

learn more… | top users | synonyms (1)

1
vote
0answers
82 views
+300

Does this proof (Lie-Kolchin) suffer from a loss of injectivity?

In the following proof (after "But there is a more elementary proof"), I was confused on something. Apparently we can assume without loss of generality that $V = V_{\chi}$. In this case, here is ...
2
votes
1answer
209 views
+50

Show norm preserving property and determine Eigenvalues

Can someone of you give me a solution for this? Let $N\in \mathbb N$. a) We define the map $\mathfrak F:(\mathbb C^N, ||\cdot||_2)\to(\mathbb C^N, ||\cdot||_2)$ by $$(\mathfrak F(x))_k := \frac{...