"Eigenvalue" Pronounce,Meaning And Examples
"Eigenvalue" Natural Recordings by Native Speakers
"Eigenvalue" Meaning
An eigenvalue is a scalar that characterizes the amount of change applied to a linear transformation. In simple terms, it is a value that is associated with a square matrix, and it represents how the matrix affects the inputted data.
When a matrix A is applied to a vector v, the resulting vector Av is scaled by some factor. This factor is the eigenvalue of the matrix A corresponding to the eigenvector v. In other words, if v is an eigenvector of A with eigenvalue λ, then Av λv.
Eigenvalues are used extensively in many areas of mathematics, science, and engineering. Some of the applications include linear algebra, differential equations, Markov chains, and signal processing.
For instance, in physics, eigenvalues can be used to describe the energy levels of a system. In computer science, eigenvalues can be used for clustering and dimensionality reduction.
In summary, eigenvalues are a fundamental concept in linear algebra that help us understand how matrices transform vectors, and they have numerous applications in various fields.
"Eigenvalue" Examples
Usage Examples of Eigenvalue
1. In Linear Algebra
The eigenvalue of a square matrix is a scalar value that represents the amount by which a linear transformation changes the shape of a geometric object.2. In Physics
In quantum mechanics, eigenvalues describe the energy levels of an atomic or subatomic system.3. In Statistics
In principal component analysis, an eigenvalue represents the amount of variability explained by each principal component.4. In Economics
Eigenvectors and eigenvalues are used in econometrics to analyze the stability of economic systems and identify the most sensitive parameters.5. In Control Theory
Eigenvalues are used to analyze the stability and controllability of control systems, such as electronic circuits or mechanical systems."Eigenvalue" Similar Words
Eidolons
Eidolons are plural nouns that refer to phantom or shadowy images, particularly of people. It is often used metaphorically to describe people's aspirations, ideals, or goals that seem elusive or intangible. The word "eidolon" can also imply a sense of illusion or fabrication, suggesting that these idealized images may not be entirely real or substantial.
Eidonomy
Eidonomy refers to the study of the relationship between names and reality. It is a branch of linguistics that examines the connection between the way we name things and the way they exist in the world. Eidonomy can help us understand how our language influences our perception of reality and how our understanding of reality shapes our language.
Eidos
The word "eidos" is a Greek term that refers to a form or appearance, especially in philosophy. In Western philosophy, eidos was used to describe the idea of a universal or eternal form that underlies the imperfect and changing world we experience through our senses. This concept is closely related to the philosopher Plato's theory of forms, which posits that there is a higher, eternal realm of abstract Forms or Ideas that are the true and eternal reality, and that the world we experience is only an imperfect reflection of these Forms. In other words, eidos refers to the abstract, ideal, or essential nature of something, rather than its physical appearance or manifestation.
Eidson
Eiffel
The Eiffel Tower is a iconic iron lattice tower located in Paris, France. It was built for the 1889 World's Fair and stands 324 meters tall. It was named after its designer, Gustave Eiffel, and has become a symbol of French culture and engineering.
Eigen
The word "eigen" has several meanings depending on the context. Here are a few common ones:<br><br>1. In mathematics, "eigen" refers to something that remains unchanged after a transformation, such as a vector or a linear transformation. For example, the eigenvalue of a matrix is a scalar that, when multiplied by the matrix, results in a new matrix that is proportional to the original matrix.<br><br>Example sentence: "The eigenvectors of the matrix represent the directions that are unchanged under the transformation."<br><br>2. In physics and chemistry, "eigen" refers to a characteristic property or feature of a system that remains unchanged under certain conditions. For example, the eigenvalue of a quantum mechanical Hamiltonian represents the energy of a system that is unchanged under a particular symmetry operation.<br><br>Example sentence: "The energy eigenstates of the atom represent the possible orientations of the atom that are unchanged under rotation."<br><br>3. In biology, "eigen" can refer to a characteristic or trait that is unchanged under certain conditions, such as environmental factors. For example, the genomic eigenvalue of an organism represents the parts of the genome that are most important for its survival and reproduction.<br><br>Example sentence: "The genomic eigenvalues of the species represent the regions of the genome that are most evolutionarily conserved."<br><br>In general, the word "eigen" refers to something that is intrinsic or fundamental to a system or entity, and remains unchanged under certain transformations or conditions.
Eigenfunction
An eigenfunction is a function that, when acted upon by a linear operator, is scaled or transformed. In other words, it is a function that is unchanged except for a scaling or change of sign when multiplied by a constant, which is the eigenvalue of the linear operator.
Eigengrau
Eigengrau is a term used to describe the grey or grayish color that the brain typically perceives when the eyes are closed in a dark or dimly lit environment. It is also referred to as the "independent grey" or "native gray".
Eigenvector
Eiger
The Eiger is a major mountain in the Bernese Alps, Switzerland, and is one of the most iconic and daunting climbs in the world. It is known for its treacherous north face, which is one of the most difficult technical climbs in mountaineering. The Eiger is often referred to as the "Eiger North Face" or simply "The Eiger" and is considered a Mecca for serious mountaineers.
Eighteen
Eighteen is a number that comes after seventeen and before nineteen. It is the age of majority in some countries, indicating that a person is considered an adult and has full legal rights and responsibilities. It can also refer to a period of time, such as the late teens, or used as a quantity, as in "eighteen people came to the party".
Eighteenth
Eighth
The word "eighth" is an adjective or adverb that refers to the number 8 or a place, position, or time that is eight in a series or sequence. It can be used to describe something that comes after the seventh item or event and before the ninth. For example:<br><br> "The eighth team to qualify for the tournament is France."<br> "The eighth grade students went on a field trip to the museum."
Eighties