1. The problem statement, all variables and given/known data The equation of a quadric surface takes the form [tex]a_i_jx_ix_j = 1, a_i_j = a_j_i[/tex] relative to the standard coordinate axes. Under a rotation of axes the equation of the surface becomes [tex]a'_i_jx'_ix'_j = 1[/tex] By considering the coordinates [tex]x_i[/tex] as components of position vectors, show that the coefficients [tex]a_i_j[/tex] are components of a second order tensor (i) using transformation laws; (ii) using the quotient theorem 2. Relevant equations 3. The attempt at a solution I need a bit of a kick-start on this one. I'm guessing my objective will be to show that: [tex]a'_i_j = l_i_ml_j_na_m_n[/tex] where [tex]l_i_j[/tex] is an entry in the matrix representing the rotation. but it's not clear to me how to relate a, l and x.