Examples of using Eigenvalues in English and their translations into Ukrainian
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Then the energy eigenvalues:.
The eigenvalues have negative real parts.
In both cases, all eigenvalues are real.
Eigenvalues and eigenvectors of the second derivative.
The diagonal entries of this matrix are the eigenvalues of T{\displaystyle T}.
Asymptotic expansions of eigenvalues and eigenfunctions of vibrating system with stiff and light-weight inclusions.
And can be represented by asingle vector equation involving two solutions as eigenvalues:.
A'' is a3×3 matrix with 3 different eigenvalues; therefore, it is diagonalizable.
We find the energy eigenvalues?? and the corresponding eigenfunctions for a particle in a one-dimensional infinitely deep potential well.
But a matrix is positive definite when andonly when all its eigenvalues are positive.
This calculator allows to find eigenvalues and eigenvectors using the Characteristic polynomial.
In the first row places values for the current node(the eigenvalues, excluding child nodes).
The matrix B does not have any real eigenvalues, so there is no real matrix Q such that Q- 1BQ is a diagonal matrix.
Therefore, to find the local maxima and minima, it suffices, theoretically,to compute the zeros of the gradient and the eigenvalues of the Hessian matrix at these zeros.
Note that if there are exactly n distinct eigenvalues in an n×n matrix then this matrix is diagonalizable.
The eigenvalues of this matrix can be used to implement a multivariable analogue of the second derivative test.(See also the second partial derivative test.).
For other well-known cases, see the main article eigenvalues and eigenvectors of the second derivative.
Therefore, to find the local maxima and minima of a differentiable function, it suffices, theoretically,to compute the zeros of the gradient and the eigenvalues of the Hessian matrix at these zeros.
Incomplete equilibrium occurs when at least one of the eigenvalues of the kinetic coefficients matrix became zero(degenerate matrix).
Equivalently, these singular vectorsare the eigenvectors corresponding to the p largest eigenvalues of the sample covariance matrix of the input vectors.
The possible results of a measurement are the eigenvalues of the operator representing the observable – which explains the choice of Hermitian operators, for which all the eigenvalues are real.
An n×n matrix A is diagonalizable over the field F if it has n distinct eigenvalues in F, i.e. if its characteristic polynomial has n distinct roots in F;
The possible results of a measurement are the eigenvalues of the operator- which explains the choice of Hermitian operators-- all their eigenvalues are real.
A linear map T: V→ V with n= dim(V)is diagonalizable if it has n distinct eigenvalues, i.e. if its characteristic polynomial has n distinct roots in F.
Λ is an eigenvalue of matrix A.
Thus λ is an eigenvalue of the matrix A.
Since the red vector was neither stretched nor compressed, its eigenvalue is 1.
Indeed, C{\displaystyle C} has one eigenvalue(namely zero) and this eigenvalue has algebraic multiplicity 2 and geometric multiplicity 1.
Be the eigenvector associated to eigenvalue λ 1{\displaystyle\lambda_{1}}.