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abcd adjugate algebra arbitrary binary forms bracket factors called Cayley co-factors co-ordinates cogredient commutative law compound concomitant contragredient convolved covariant cubic currency definition degree denote derangement determinant of order differential dx dy elements equal equivalent symbols example expand expressed follows form F formal dual function fundamental identity Fundamental Theorem given gives ground forms Hence homogeneous homogeneous co-ordinates inner product integers interchange invariant invariant theory involving Jacobian Laplace development leading diagonal letters linear equations linear form linear transformation Math minant multilinear form multiplying notation obtain operator ordinary numbers orthogonal matrix orthogonal transformation p-ic polar polynomial proof proves the theorem quadratic quadric quartic rank reciprocal result rows and columns scalar sets of variables Similarly skew symmetric square matrix ternary ternary forms theorem of corresponding theory transposition unit matrix vanish identically vectors write written yv y2 zero