Consider the linear transformation S : Mn(R) Mn(R) defined by S(A) = A + AT , where A is
Chapter 6, Problem 13(choose chapter or problem)
Consider the linear transformation S : Mn(R) Mn(R) defined by S(A) = A + AT , where A is a fixed n n matrix. (a) Find Ker(S) and describe it. What is dim[Ker(S)]? (b) In the particular case when A is a 2 2 matrix, determine a basis for Ker(S), and hence, find its dimension.
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