Form a matrix without using column indexes.

I want to represent a matrix
$$ Gamma = ( gamma_1, gamma_2, cdots, gamma_p) $$
or
$$ gamma_j = ( lambda b_j-X_j Xb) / (X_j_X_j- lambda) $$
$$ X = (X_1, X_2, cdots, X_p) $$
$ lambda $ is a constant.

How to represent the matrix $ Gamma $ without $ gamma_j $.