Explore Eigenvalues through 10+ example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.
Eigenvalues meaning
plural of eigenvalue
Using Eigenvalues
- The main meaning on this page is: plural of eigenvalue
- In the example corpus, eigenvalues often appears in combinations such as: the eigenvalues, eigenvalues of, eigenvalues are.
Context around Eigenvalues
- Average sentence length in these examples: 21.7 words
- Position in the sentence: 8 start, 8 middle, 4 end
- Sentence types: 19 statements, 1 questions, 0 exclamations
Corpus analysis for Eigenvalues
- In this selection, "eigenvalues" usually appears near the start of the sentence. The average example has 21.7 words, and this corpus slice is mostly made up of statements.
- Around the word, same, moduli and satisfy stand out and add context to how "eigenvalues" is used.
- Recognizable usage signals include eigenvalues and eigenvectors and all its eigenvalues are positive. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "eigenvalues" sits close to words such as aaf, aalen and abrogated, which helps place it inside the broader word index.
Example types with eigenvalues
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
A Hermitian matrix is positive definite if all its eigenvalues are positive. (12 words)
Care must be taken since some of the eigenvalues could have the same magnitude. (14 words)
For a flow, it will occur when there are eigenvalues on the imaginary axis. (14 words)
When the eigenvalues of J are not in the unit circle, the dynamics near the fixed point x 0 of F is called hyperbolic and when the eigenvalues are on the unit circle and complex, the dynamics is called elliptic. (40 words)
Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonian (of a bound system ) in quantum mechanics that measures the energy levels, which are called the eigenvalues. (31 words)
For computing the weights and nodes, it is preferable to consider the symmetric tridiagonal matrix with elements : J and are similar matrices and therefore have the same eigenvalues (the nodes). (30 words)
Eigenvalues are closely related to vibration frequencies and are used in analyzing a famous problem: can you hear the shape of a drum? (23 words)
Example sentences (20)
Eigenvalues and eigenvectors The eigenvalues of the DFT matrix are simple and well-known, whereas the eigenvectors are complicated, not unique, and are the subject of ongoing research.
Operators on infinite-dimensional Hilbert spaces need not have eigenvalues (the set of eigenvalues does not necessarily coincide with the spectrum of an operator ).
This means that the eigenvalues satisfy the equation: : Therefore, the eigenvalues of are the fourth roots of unity : is +1, −1, +i, or −i.
When the eigenvalues of J are not in the unit circle, the dynamics near the fixed point x 0 of F is called hyperbolic and when the eigenvalues are on the unit circle and complex, the dynamics is called elliptic.
Like proving that if a matrix is diagonalizable and only has eigenvalues of -1 and 1, then its inverse matrix is also diagonalizable.
A Hermitian matrix is positive definite if all its eigenvalues are positive.
And the eigenvectors corresponding to these eigenvalues are: : Only the eigenvalue is more than unity.
As in the continuous case, the eigenvalues and eigenvectors of A determine the structure of phase space.
Care must be taken since some of the eigenvalues could have the same magnitude.
Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonian (of a bound system ) in quantum mechanics that measures the energy levels, which are called the eigenvalues.
Eigenvalues and eigenvectors main In general, the action of a linear transformation may be quite complex.
Eigenvalues are closely related to vibration frequencies and are used in analyzing a famous problem: can you hear the shape of a drum?
For a flow, it will occur when there are eigenvalues on the imaginary axis.
For a map, the bifurcation will occur when there are eigenvalues of DF μ on the unit circle.
For computing the weights and nodes, it is preferable to consider the symmetric tridiagonal matrix with elements : J and are similar matrices and therefore have the same eigenvalues (the nodes).
From the eigenvalues and the eigenvectors of A it is possible to determine if an initial point will converge or diverge to the equilibrium point at the origin.
Hence * If is normal then *: where and are maximal and minimal (by moduli) eigenvalues of respectively.
If a and b are positive, the eigenvalues are all positive, and the solutions are trigonometric functions.
If all of the eigenvalues are positive, then the point is a local minimum; if all are negative, it is a local maximum.
If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum.
Common combinations with eigenvalues
These word pairs occur most frequently in English texts:
- the eigenvalues 19×
- eigenvalues of 13×
- eigenvalues are 8×
- eigenvalues and 5×
- eigenvalues the 3×
- energy eigenvalues 3×
- of eigenvalues 2×
- its eigenvalues 2×
- are eigenvalues 2×