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In the same way, we can define derivatives of matrix-valued operators as linear operators on matrices. For example, f(X)=X² gives f'(X)[dX] = X dX + dX X. Or f(X) = X⁻¹ gives f'(X)[dX] = –X⁻¹ dX X⁻¹.

2) Steady States: Find the steady states of the ODE. 3) Linearization: Compute the Jacobian matrix, which provides a linearization of the dynamics around the steady state. Once the Jacobian has been ...

There is currently no systematic way of learning the Jacobian matrix using DNNs and deploy it online for task space control in a stable manner without additional offline training for each task. This ...

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