characteristic equation वाक्य
उदाहरण वाक्य
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- A prime \ ell is called an Elkies prime if the characteristic equation of the Frobenius endomorphism, \ phi ^ 2-t \ phi + q = 0, splits over \ mathbb { F } _ \ ell.
- Note that the characteristic equation for a rotation is a quadratic equation with discriminant D =-4 ( \ sin \ theta ) ^ 2, which is a negative number whenever \ theta is not an integer multiple of 180?
- Comparing the terms of this equation with those of the desired characteristic equation yields the values of the feedback matrix \ textbf { K } which force the closed-loop eigenvalues to the pole locations specified by the desired characteristic equation.
- Comparing the terms of this equation with those of the desired characteristic equation yields the values of the feedback matrix \ textbf { K } which force the closed-loop eigenvalues to the pole locations specified by the desired characteristic equation.
- Lawson also clearly showed that since the coefficients of the characteristic equation represented the principal minor of the network matrix and loop analysis was basically the calculation of all possible principal minors that the extraction of the eigenvectors provided the same stability analysis with little computational effort.
- The Laplace transform finds wide application in physics and particularly in electrical engineering, where the characteristic equations that describe the behavior of an electric circuit in the complex frequency domain correspond to linear combinations of exponentially damped, scaled, and time-shifted sinusoids in the time domain.
- The stability condition stated above in terms of eigenvalues for the second-order case remains valid for the general " n " th-order case : the equation is stable if and only if all eigenvalues of the characteristic equation are less than one in absolute value.
- If the other roots of the characteristic equation lie inside the unit circle that is, have a modulus ( absolute value ) less than one then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary.
- Therefore, from the characteristic equation, the coefficients I _ 1, I _ 2 and I _ 3, called the first, second, and third " stress invariants ", respectively, always have the same value regardless of the coordinate system's orientation.
- So, we have t an eigenvalue of Q and t ^ {-1 } an eigenvalue of Q ^ {-1 } but as these two matrices have the same characteristic equation, we must have t and its inverse being equal, ie plus or minus one.
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