Linear dynamical system

Linear dynamical systems are dynamical systems whose evaluation functions are linear. While dynamical systems in general do not have closed-form solutions, linear dynamical systems can be solved exactly, and they have a rich set of mathematical properties. Linear systems can also be used to understand the qualitative behavior of general dynamical systems, by calculating the equilibrium points of the system and approximating it as a linear system around each such point.

In a linear dynamical system, the variation of a state vector (an ${\displaystyle N}$-dimensional vector denoted ${\displaystyle \mathbf {x} }$) equals a constant matrix (denoted ${\displaystyle \mathbf {A} }$) multiplied by ${\displaystyle \mathbf {x} }$. This variation can take two forms: either as a flow, in which ${\displaystyle \mathbf {x} }$ varies continuously with time

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