What is a sufficient criteria for testing whether or not a set of matrices span the Lie algebra of $SL_{2}(\mathbf{R})$?
Spanning the Lie Algebra of $SL_{2}(\mathbf{R})$
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linear-algebra
representation-theory
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0Finding three linearly independent ones? – 2011-10-12
2 Answers
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There should be as many matrices as the algebra, be elements of the algebra and they should be linearly independent.
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One condition is that they not have a common one-dimensional invariant subspace in $\mathbb C^2$.