For a second-order linear autonomous system, a characteristic equation has one positive and one negative real eigenvalue.
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Given a rotation matrix " M " the eigenvalues can calculated by solving the characteristic equation for that matrix.
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The frequency that appears in the generalised form of the characteristic equation ( which is the same for this circuit as previously)
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If the solution is to be used numerically, all the roots of this characteristic equation can be found by numerical methods.
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The roots ? of the characteristic equation are called characteristic roots or eigenvalues and the solution set is often referred to as the spectrum.
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The semi-implicit method models the simulated system correctly if the complex roots of the characteristic equation are within the circle shown below.
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The classical Liouville equation can be solved using the method of characteristics for partial differential equations, the characteristic equations being Hamilton's equations.
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The original equations have been decoupled into N + 2 characteristic equations each describing a simple wave, with the eigenvalues being the wave speeds.
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These quantities are inter-related by one or more functional relationships called equations of state, and by the system's characteristic equation.
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The qualities of the Euler's characteristic equation were later considered in greater detail by French mathematicians Augustin-Louis Cauchy and Gaspard Monge.
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