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You can also use SparseArray as follows
SparseArray
sa[n_] := SparseArray[{{1, _}|{_, 1}|{i_, j_i_} /; i > j1 -> 1 - i, {i_, i_j_} /; 1 < i >< 1j -> 1 - i0}, {n, n}], 1] matrix2 = sa[7] matrix2 == matrix
True
sa[n_] := SparseArray[{{1, _}|{_, 1}|{i_, j_} /; i > j -> 1, {i_, i_} /; i > 1 -> 1 - i}, {n, n}] matrix2 = sa[7] matrix2 == matrix
sa[n_] := SparseArray[{{i_, i_} /; i > 1 -> 1 - i, {i_, j_} /; 1 < i < j -> 0}, {n, n}, 1] matrix2 = sa[7] matrix2 == matrix
