Normaliziation and Scaling of a Second Order System

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I understand how to normalize a second order system, but I wanted to know if the same steps are taken when the parameters of the system are not scalar but matrices. For example
where the parameter phi, and gamma are both 3x3 matrices and X is a 3x1 vector.
The solution i've come up with is:
where omega is equal to the square root of the inverse of gamma, and x the new dimensionless parameter.
I will upload a photo of all my steps if necessary, but I really just wanted to know if this problem can be approached exactly the same way as you would for a second order system with scalar parameters.
Or if I'm way off in general that'd be nice to know..

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