Examples of using Eigenvalues in English and their translations into Chinese
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Spectrum and eigenvalues.
The eigenvalues of the covariance matrix can easily be shown to be.
What will happen when eigenvalues are roughly equal?
The diagonal entries of this matrix are the eigenvalues of T.
It is easy to see that the eigenvalues lie in the approximate point spectrum.
In the 2D case, we obtain two eigenvectors and two eigenvalues.
Thus, a and b are the eigenvalues corresponding to u and v, respectively.
(A limiting case of type VI where both eigenvalues are equal.).
And Eigenvalues for non-linear systems and Special trigonometric Functions.
Suppose that we want to compute the eigenvalues of a given matrix.
The left Cauchy-Green deformationtensor also has the principal stretches as eigenvalues.
If it does not equal -1, some eigenvalues and all eigenvectors are meaningless.
This is the case when M is nilpotent butnot 0(eigenvalues all 0).
He also showed, in 1829, that the eigenvalues of symmetric matrices are real.
The right Cauchy-Green deformationtensor also has the principal stretches as eigenvalues.
Having determinant±1 and all eigenvalues of magnitude 1 is of great benefit for numeric stability.
But a matrix is positive definite when andonly when all its eigenvalues are positive.
Eigenvalues: In discussing their approach to time travel, Tony Stark and Bruce Banner mention eigenvalues.
Not every matrix can be decomposed into eigenvalues and eigenvectors.
However an operator on an infinite-dimensional space may have additional elements in its spectrum,and may have no eigenvalues.
Not every matrix can be decomposed into eigenvalues and eigenvectors.
Note: For a regular structure with eigenvalues in only one direction, only one shear force for the considered direction will be obtained.
Thus the spectrum of an operator always contains all its eigenvalues, but is not limited to them.
In this case, the term eigenvector is used in a somewhat more general meaning,since the Fock operator is explicitly dependent on the orbitals and their eigenvalues.
This is most likely anexample of movie math talk for effect, as eigenvalues are a fairly low-level(basic) concept in linear algebra.
However, non-convex problems can have much more complicated landscapes that involve degenerate saddle points-points whose Hessian is positive semidefinite and have 0 eigenvalues.
The continuous spectrum therefore consists of those approximate eigenvalues which are not eigenvalues and do not lie in the residual spectrum.
Normally, physicists describe quantum systems using highly symmetric mathematical matrices whose solutions,or“eigenvalues,” correspond to the system's energy levels.