2
$\begingroup$

What is a sufficient criteria for testing whether or not a set of matrices span the Lie algebra of $SL_{2}(\mathbf{R})$?

  • 0
    Finding three linearly independent ones?2011-10-12

2 Answers 2

3

There should be as many matrices as the algebra, be elements of the algebra and they should be linearly independent.

2

One condition is that they not have a common one-dimensional invariant subspace in $\mathbb C^2$.