eigenvalue Synonyms

No Synonyms and anytonyms found

eigenvalue Meaning

Wordnet

eigenvalue (n)

(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant

eigenvalue Sentence Examples

1. The eigenvalue of the matrix A determines the magnitude of its corresponding eigenvector's scaling.
2. The eigenvalues of a Hamiltonian operator represent the possible energy levels of a system.
3. The eigenvalue equation highlights the relationship between an operator and its eigenfunction, where the eigenvalue specifies the scaling factor.
4. Eigenvalues are critical in stability analysis, indicating the rate of decay or growth of system oscillations.
5. The characteristic equation of a matrix provides the eigenvalues that govern the system's behavior.
6. The largest eigenvalue of a transition matrix determines the long-term behavior of a Markov chain.
7. In quantum mechanics, eigenvalues represent the observable values of a physical property, such as energy or angular momentum.
8. Eigenvalues arise in various mathematical and scientific disciplines, including linear algebra, quantum physics, and vibration analysis.
9. The calculation of eigenvalues and eigenvectors is essential for understanding the dynamics of complex systems.
10. Eigenvalue analysis serves as a powerful tool for uncovering the fundamental properties of linear operators and their associated transformations.

FAQs About the word eigenvalue

What is the meaning of the word eigenvalue

(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant

What are the synonyms of the word eigenvalue

No synonyms found.

What are the antonyms of the word eigenvalue

No antonyms found.

What is the usage of word eigenvalue

The eigenvalue of the matrix A determines the magnitude of its corresponding eigenvector's scaling.

The eigenvalues of a Hamiltonian operator represent the possible energy levels of a system.

How to use the word eigenvalue in a sentence?

The eigenvalue equation highlights the relationship between an operator and its eigenfunction, where the eigenvalue specifies the scaling factor.

Eigenvalues are critical in stability analysis, indicating the rate of decay or growth of system oscillations.