Question

if A_{ij} is a skew-symmetric tensor,then show that (B^i_jB^k_p+B^i_pB^k_j)A_ik=0

Answer 1

Question 19020

For skew-symmetric tensor $A_{ik} = -A_{ki}$ . Hence,

$$B _ {i j} B _ {k p} A _ {i k} + B _ {i p} B _ {k j} A _ {i k} = B _ {i j} B _ {k p} A _ {i k} + B _ {k p} B _ {i j} A _ {k i} = B _ {i j} B _ {k p} A _ {i k} - B _ {k p} B _ {i j} A _ {i k} = 0.$$