Orthonomalization with respect mass matrix

Let  be the correction mode vector and  be the orthonormalized correction mode vector with respect to , then  can be represented as

                            (1)

where  denotes the p-th vibration normal mode. Gram Schmidt orthogonalization procedure can be used to remove the vibration normal modes from the correction mode. The othonomalized correction mode must satisfy the following equation.

               (2)

Since  is orthonomal to,   can be obtained as follows:

                     (3)

Substitution of the above equation into Equation (1) gives the orthonormalized correction mode.