Thread: Help me in understanding reseach paper

1. Help me in understanding reseach paper

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

2. Originally Posted by maken83
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.

3. Originally Posted by maken83
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