 
 Try the examples in this order. 

 (You can compile the *.c files directly without create a project)


          Is T a linear transformation?  
          ============================

 tu01.c    T : R**3 -> R,    T(x1,x2,x3) = (x1 + x2 + x3)   
             
 tu02.c    T : R**3 -> R**2, T(x1,x2,x3) = (2x1 - x2 + x3, x2 - 4x3)  

 tu03.c    T :    V -> R,            Euclidean Inner Product on R**n

 tu04.c    T : R**n -> R,    Weighed Euclidean Inner Product on R**n  
 
 tu05.c    T : R**n -> R,    Inner Product on R**n generated by A


 tA01a.c   T : Mnxn -> R,    T(A) = trace(A)
 tA01b.c       Is T(0)     =  0           ?
 tA01c.c       Is T(-A)    = -T(A)        ?
 tA01d.c       Is T(A - B) =  T(A) - T(B) ?

 tA02a.c   T : Mnxn -> R,    T(A) = Matrix Inner Product on Mnxn         
 tA02b.c       Is T(0)     =  0           ?
 tA02c.c       Is T(-A)    = -T(A)        ?
 tA02d.c       Is T(A - B) =  T(A) - T(B) ?

 tA03a.c   T : Mnxp -> Mnxq, T(A) = AX         
 tA03b.c       Is T(0)     =  0           ?
 tA03c.c       Is T(-A)    = -T(A)        ?
 tA03d.c       Is T(A - B) =  T(A) - T(B) ?
