hkus10 Posted March 19, 2011 Share Posted March 19, 2011 Let T be the set of all matrics of the form AB - BA, where A and B are nxn matrics. Show that span T is not Mnn. 1) does "span T is not Mnn" mean that Mnn does not span T? Thanks Link to comment Share on other sites More sharing options...

DrRocket Posted March 20, 2011 Share Posted March 20, 2011 Let T be the set of all matrics of the form AB - BA, where A and B are nxn matrics. Show that span T is not Mnn. 1) does "span T is not Mnn" mean that Mnn does not span T? Thanks No it means that the set of all linear combinations of elements of T does not include all of Mnn. One presumes that by Mnn you mean all nxn matrices, so the problem is to show that the space spanned by commutators is not all linear operators on n-space. To do that you might want to look for an invariant shared by commutators that is not a property of all operators. Link to comment Share on other sites More sharing options...

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