The following thing is what comes me to mind, I hope it is correct.

So, a hexagonal matrix has the following form:

g_hex = [ a^2 -0.5*a^2 0

-0.5*a^2 a^2 0

0 0 c^2]

where a,c and the lattice parameters. (c - vertical parameter)

A tetragonal matrix has the form:

g_tet = diag(d^2, e^2, f^2)

where d,e,f are the lattice parameters

So, we need the transformation matrix T:

G_tet = T * g_hex * T_transpose

From here it is an easy task to find the T matrix. Hope I helped.

thank you sir for your help. Could you suggest any books or links for finding transformtion matrix for converting between lattices