How do you use Eigenvalue in a sentence? See 10+ example sentences showing how this word appears in different contexts, including synonyms like value, plus the exact meaning.
Eigenvalue meaning
A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
Synonyms of Eigenvalue
Using Eigenvalue
- The main meaning on this page is: A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
- Useful related words include: value.
- In the example corpus, eigenvalue often appears in combinations such as: eigenvalue is, the eigenvalue, same eigenvalue.
Context around Eigenvalue
- Average sentence length in these examples: 20 words
- Position in the sentence: 3 start, 12 middle, 5 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Eigenvalue
- In this selection, "eigenvalue" usually appears in the middle of the sentence. The average example has 20 words, and this corpus slice is mostly made up of statements.
- Around the word, same, associated, particular, analysis, corresponds and concept stand out and add context to how "eigenvalue" is used.
- Recognizable usage signals include a particular eigenvalue of f and an associated eigenvalue which is. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "eigenvalue" sits close to words such as aal, aalto and aardvark, which helps place it inside the broader word index.
Example types with eigenvalue
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
If one eigenvalue is negative (i. (6 words)
This is a contradiction, and so A has an eigenvalue. (10 words)
The corresponding eigenvalue is the factor by which the eigenvector is scaled. (12 words)
Assuming that the matrix W is a primitive matrix ( irreducible and aperiodic ), then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate. (35 words)
This theorem is ultimately connected with the spectral characterization of as the eigenvalue associated with the Heisenberg uncertainty principle, and the fact that equality holds in the uncertainty principle only for the Gaussian function. (34 words)
The set of all eigenvectors corresponding to a particular eigenvalue of f forms a vector space known as the eigenspace corresponding to the eigenvalue (and f ) in question. (28 words)
Example sentences (20)
Moreover, the eigenvectors are not unique because any linear combination of eigenvectors for the same eigenvalue is also an eigenvector for that eigenvalue.
The set of all eigenvectors corresponding to a particular eigenvalue of f forms a vector space known as the eigenspace corresponding to the eigenvalue (and f ) in question.
The corresponding eigenvalue is the factor by which the eigenvector is scaled.
A natural way to do this is by eigenvalue analysis of a matrix.
And the eigenvectors corresponding to these eigenvalues are: : Only the eigenvalue is more than unity.
Assuming that the matrix W is a primitive matrix ( irreducible and aperiodic ), then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate.
Definition The plot of von Neumann entropy Vs Eigenvalue for a bipartite 2-level pure state.
Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.
Essentially an eigenvalue is like a note being played by the manifold.
For a diagonal matrix, this is true only if each element of the main diagonal—that is, every eigenvalue of M—is positive.
Here λ is an associated eigenvalue, which is constrained by Sturm–Liouville theory to take on only certain specific values.
If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest.
If one eigenvalue is negative (i.
In functional analysis, the concept of the spectrum of a bounded operator is a generalization of the eigenvalue concept for matrices.
So appears as an optimal constant in Wirtinger's inequality, and from this it follows that it is the smallest such eigenvalue (by Rayleigh quotient methods).
The multiplicity gives the number of linearly independent eigenvectors corresponding to each eigenvalue.
Then is an energy eigenket with the same eigenvalue, since : Since U is nontrivial, at least one pair of and must represent distinct states.
The value is in fact the least such eigenvalue, and is associated with the fundamental mode of vibration of the string.
This is a contradiction, and so A has an eigenvalue.
This theorem is ultimately connected with the spectral characterization of as the eigenvalue associated with the Heisenberg uncertainty principle, and the fact that equality holds in the uncertainty principle only for the Gaussian function.
Common combinations with eigenvalue
These word pairs occur most frequently in English texts:
- eigenvalue is 6×
- the eigenvalue 4×
- same eigenvalue 2×
- eigenvalue of 2×
- eigenvalue and 2×
- associated eigenvalue 2×
- an eigenvalue 2×
- one eigenvalue 2×
- such eigenvalue 2×