- #1
rarkup
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Homework Statement
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
Homework Equations
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.