ABSTRACT
Since the matrix B is symmetric-it represents the second-order partial derivatives of f-there exists a unitary matrix U such that
where D is a diagonal matrix.23 Then let v=Ux; this is a rotation of the basis vectors in n-space. Substituting this, along with equation (88), into equation (87),
Write D=diag(?1, …, ?n) and define g=Ua. We get a much simpler equation
Transforming the independent variables further by
