explanation.txt

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\textrm{\CY{System dynamics}depend on a \CR{linear transformation}of} \\
\textrm{its current state plus a term} \\
\textrm{which describes the influence of \CB{external inputs}}
\\~\\

\textrm{the solution to this differential equation looks like}
\\~\\
x_1(t) = \CL{x_1(0)} \, e^{\CR{\lambda_1} t}
\\~\\

\textrm{the real part of the \CR{eigenvalues}scale the rate of decay}\\
\textrm{for trajectories of } x(t) \textrm{ in the direction of} \\
\textrm{the associated eignevector.}

\\~\\
\textrm{the imaginary part of the \CR{eigenvalues}scale the rate of oscillation}\\
\textrm{for trajectories of } x(t)
\\~\\