Matrix Exponential
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms — Solution via Matrix Exponential
From the book
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms. In the chapter mind map this icon labels Solution via Matrix Exponential:$e^{At}$. The discussion below is excerpted and lightly edited from § Solution via Matrix Exponential in Mathematics for AI and Machine Learning.
The solution to the state equation with initial condition $\mathbf{h}(0) = \mathbf{h}_0$ is (see the matrix chapter, equation @eq:linear-ode-solution):
The first term is the homogeneous solution (response to initial conditions), and the second is the particular solution (response to input).
What this drawing shows
What you see. Represents exp(A), the operator used to solve linear differential equations.
In the mind map. Chapter 20 — Solution via Matrix Exponential. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 20: ODE, SDE, and Continuous Limits of Algorithms — see the mind-map node Solution via Matrix Exponential.
