What is the solution to the matrix differential equation dx/dt = Ax with initial condition x(0) = x₀?
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x(t) = e^(At)x₀
The matrix exponential e^(At) is defined via a power series. It generalizes the scalar exponential solution to systems of linear differential equations.
Also asked as:
- What is the solution for a system of linear differential equations defined by dx/dt = Ax, given an initial state x₀?