Associate Tensors and Affine Connections

Let a_ij be any given non-singular symmetric tensor. Then if g_ij is any other non-singular symmetric tensor, we can construct, with the help of a_ij, another non-singular symmetric tensor Ãg_ij defined by

g_ij = a_is a_jt g^st; so g_ij = a_is a_jt g^st, (1.1)