a discrete group is said to be inner amenable if it admits an atomless mean which is invariant under conjugation. in this talk i will provide a satisfying characterization of inner amenability for linear groups over an arbitrary field. i will also discuss a complete characterization of linear groups which are stable in the sense of jones and schmidt. the analysis of stability leads to many new examples of (non-linear) stable groups; notably, all nontrivial countable subgroups of monod's group h(r) are stable. this includes nonamenable groups constructed by monod and by lodha and moore, as well as thompson's group f.