If $H(t)$ is a given two dimensional Hamiltonian matrix , $Y$ is a vector (spinor). Defined is the function $F(t,Y)= H(t)Y$. What is the Jacobian of F(t,Y). In some numerical method I need to find the approximate Jacobian defined by $\frac{\partial F}{\partial Y}(t_0, Y_0)$ which I am using in an implicit Runge-Kutta scheme. For example suppose that the problem is like this: \begin{equation} F(t, Y) = \begin{pmatrix} t^2 & t+5\\ exp(t^2) & ln(t) \end{pmatrix} \begin{pmatrix} Y_1 \\ Y_2 \end{pmatrix} \end{equation} How can I find the Jacobian $\frac{\partial F}{\partial Y}$?
2026-03-25 06:05:50.1774418750
How to find the Jacobian of a matrix vector product?
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