Examples of using Eigenvalues in English and their translations into Serbian
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All the eigenvalues are distinct.
An exception occurs when R has eigenvalues equal to- 1.
Eigenvalues are obtained by solving.
Hence has no eigenvalues and so.
And when the borderline is tau equals zero, the eigenvalues are…?
If it is positive,then the eigenvalues are both positive, or both negative.
If the operator's spectrum is discrete, the observable can attain only those discrete eigenvalues.
In this case we can write the eigenvalues as λ 1, λ 2= α± β i.
In two variables, the determinant can be used,because the determinant is the product of the eigenvalues.
If and only if both eigenvalues are smaller than one in absolute value.
Perform vector and matrix operations,including eigenvalues and eigenvectors.
The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
Solve for r to obtain the two roots λ1, λ2:these roots are known as the characteristic roots or eigenvalues of the characteristic equation.
The trace of a matrix is the sum of its(complex) eigenvalues(counted with multiplicities), and it is invariant with respect to a change of basis.
In this paper he gave a derivation of the wave equation for time independent systems, andshowed that it gave the correct energy eigenvalues for a hydrogen-like atom.
Their energy eigenvalues are so close together that they behave as one combined p shell, similar to the non-relativistic 2p and 3p shells.
The Hessian matrix plays an important role in Morse theory and catastrophe theory,because its kernel and eigenvalues allow classification of the critical points.[2][3][4].
If both the eigenvalues of the middle matrix are non-zero(i.e. it is an ellipse or a hyperbola), we can do a transformation of variables to obtain.
Besides classical and well documented applications to Chemistry,we are witnesses of the appearance of graph eigenvalues and eigenvectors in Computer Science in various investigations.
Vector spaces, eigenvalues and eigenvectors of matrices, rank of matrices, systems of linear equations, analytic geometry. Contents of exercisesPractical assignments related to the theoretical component(lectures).
NoneThe goalIntroduce students to the basic concepts of quantum mechanics,such as the Schrödinger equation, eigenvalues and eigenvectors. The outcomeUnderstanding of the quantum states descriptions by wave functions.
The stability condition stated above in terms of eigenvalues for the second-order case remains valid for the general nth-order case: the equation is stable if and only if all eigenvalues of the characteristic equation are less than one in absolute value.
With state vector x and transition matrix A,x converges asymptotically to the steady state vector x* if and only if all eigenvalues of the transition matrix A(whether real or complex) have an absolute value which is less than 1.
In all cases-real distinct eigenvalues, real duplicated eigenvalues, and complex conjugate eigenvalues-the equation is stable(that is, the variable a converges to a fixed value) if and only if both eigenvalues are smaller than one in absolute value.
NoneThe goalIntroduce students to the basic concepts of quantum mechanics,such as the Schrödinger equation, eigenvalues and eigenvectors. The outcomeUnderstanding of the quantum states descriptions by wave functions.
In all cases- real distinct eigenvalues, real duplicated eigenvalues, and complex conjugate eigenvalues- the equation is stable(that is, the variable a converges to a fixed value) if and only if both eigenvalues are smaller than one in absolute value.
In spectral graph theory we expect the result relate to all subjects quoted in the research description andespecially results in relation with extremal problems with eigenvalues for the adjacency, Laplacian and signless Laplacian natrix.
The possible results of a measurement are the eigenvalues of the operator- which explains the choice of Hermitian operators-- all their eigenvalues are real.
In the first-order matrix difference equation= A{\displaystyle=A} with state vector x and transition matrix A,x converges asymptotically to the steady state vector x* if and only if all eigenvalues of the transition matrix A(whether real or complex) have an absolute value which is less than 1.
Closely related is the invariant called the energy of a graph,which is defined as the sum of eigenvalues moduli. The planned investigations of weighted graphs have direct application in transportation. Other possible applications could be telecommunication and computer networks, transmission networks, etc.