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How do I compute the maximum values for ||M(q)|| and ||M_dot(q)||, the induced 2-norms, where M(q) is the mass matrix from the standard dynamical model of a robotic manipulator. I have the numerical values but not the analytical symbolic representation.

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I think this is an eigenvalue problem because:

  1. The mass matrix can be assumed to be PSD
  2. The induced norm of a PSD matrix is see here $\sqrt{\lambda_{max}(A^TA)}$

So for anything but the smallest matrices, you should use iterative methods to determine the norm (i.e., there is no closed-form solution).

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