If is a fixed vector, verify that a second-order tensor C can be defined by...

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If æ is a fixed vector, verify that a second-order tensor C can be defined by setting C(y) = x x y. Find the components of C and show that it is antisymmetric. Show that any antisymmetric tensor can be made equal to C by suitable choice of the fixed vector æ. If æ is a fixed vector, verify that a second-order tensor C can be defined by setting C(y) = x x y. Find the components of C and show that it is antisymmetric. Show that any antisymmetric tensor can be made equal to C by suitable choice of the fixed vector æ.