# C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes5-1 -...

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SECTION 5.1 EIGENVECTORS AND EIGENVALUESEXAMPLES.(1) Physical systems are often modeled by a state vectorvinRpwhichgives relevant measurements or properties of the system, e.g., temperature, pressure, volume,chemical concentrations, . . . , or temperature, voltage, current, . . . , or population split intoage groups or. . . .You can think of others. We can then model the evolution of the systemby a transition matrixA, so that if the current state is given byvthen the next state isgiven byAv. Of particular interest would be those steady states for whichAv=v, as wellas those states for whichAv=λvfor some scalarλ.(2) We can easily deal with vectors whose entries are functions, so that we can writex(t) =x1(t)x2(t)...xp(t).Then a system of differential equations with constant coefficients can be written asx0(t) =Ax(t) for some matrixA. When would there be a solution of the formx(t) =
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Term
Spring
Professor
PAVLOVIC
Tags
Fundamental physics concepts, chemical concentrations, EIGENVALUES EXAMPLES
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