Normalization and Scaling of second order DE

Jul 2016
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

d2X/dt2 + (2H)dX/dt + (E)X = 0

where 2H and E are 3x3 matrices and X is a 3x1 column vector.

The solution I have is

d2x/dtau2 + (2wH)dx/dtau + x = 0

where w is equal to the square root of the inverse of E, and x and tau are the new parameters.

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.



MHF Helper
Sep 2012
Hey ee89.

There are books that cover matrix based calculus and I would redirect you to those resources for more information.

I know that this is covered in graduate statistics when (generalized) linear models are involved and I imagine it's covered in over areas of applied mathematics and/or applied statistics.