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if the equality $a^i_ju_i=Ku_j$ holds for any covariant vector $u_i$ such that $u_iv^i=0$ where $v^i$ is a given contravariant vector, show that $a^i_j=K\delta^{i}_{j} +p_jv^i$.

i am completely stuck on it.how can i solve this problem?

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Related: math.stackexchange.com/questions/265167/… –  user53153 Dec 26 '12 at 7:07

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