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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: http://math.stackexchange.com/questions/265167/a-tensor-calculus-problem2012-12-26

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