The subspace spanned by { T ^ ^ i j } can be divided two subspaces; three independent antisymmetric components { A ^ ^ i j } and six independent symmetric component { S ^ ^ i j } , defined as A ^ ^ i j = 1 2 ( T ^ ^ i j − − T ^ ^ j i ) and S ^ ^ i j = 1 2 ( T ^ ^ i j + T ^ ^ j i ) . Using the { T ^ ^ i j } transformation under rotation formula, it can be shown that both { A ^ ^ i j } and { S ^ ^ i j } are transformed into a linear combination of members of its own sets. Although { A ^ ^ i j } is irreducible, the same cannot be said about { S ^ ^ i j } .