2.11. The Cross Product Expressed As A Determinant

An n´n determinant is defined as

        det| a ij |= ε i 1 i n a 1   i 1 a n   i n

The cross product C=A×B  can be written as

        C= e i ( A×B ) i   = ε ijk e i a j b k   =| e 1 e 2 e 3 a 1 a 2 a 3 b 1 b 2 b 3 |