Let A be the Algebra generated by 2×2 matrices M and N. Now if A has dimension greater than 3, then how we say it is full matrix algebra, and how we say there is no common eigenvector for the set of all element of A. Plz help me. Thanx
Let A be the Algebra generated by 2×2 matrices M and N. Now if A has dimension greater than 3, then how we say it is full matrix algebra, and how we say there is no common eigenvector for the set of all element of A. Plz help me. Thanx
The algebra of all 2 by 2 matrices has dimension 4. If A has "dimension greater then 3" then it must have dimension 4 and be the algebra of all 2 by 2 matrices. Further, it is easy to construct two 2 by 2 matrices that have no eigenvector in common.
Let A be the Algebra generated by 2cross2 matrices M and N. Now if A has dimension greater than 3, then how we say it is full matrix algebra, and how we say there is no common eigenvector for the set of all element of A. Plz help me. Thanx
Since the whole algebra of all 2x2 matrices has dimension 4, any (sub)algebra having dimension greater than 3 is the whole thing...
Tonio
Last edited by mr fantastic; May 1st 2010 at 04:53 AM.
Reason: Moved from thread created by duplicate post.