Let C^2x2 be the complex vector space of 2 x 2 matrices with complex entries. Let B= [1 -1]
and let T be the linear operator defined on C^2x2(T: C^2x2 --> C^2x2) by T(A)=BA. What is the rank of T? Can you describe T?
For this question you will need to get a basis of C^2x2 and use it to write a matrix representative of T. Recall that a linear operator is a linear transformation from some vector space V into V.
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Let be the complex vector space of matrices with complex entries. Let and let T be the linear ...
Linear transformations, vector space and basis are investigated. The rank of matrices representatives are discussed.