Let B be the matrix whose row are the standard basis, and C the matrix whose row i is the 3x1 basis vector Fi (i=1,2,3) for the coordinate system. and
p =(2/3, 2/3, 1/3)
(1/3,-2/3, 2/3)
(2/3 -1/3,-2/3)
Then
B=PT (P transpose)(C) ---(2)
Where P the transition matrix from the...