What does eigenvalue mean?
An eigenvalue is a scalar value that represents how much change occurs in a linear transformation. It is a fundamental concept in linear algebra and is used to describe the properties of matrices and linear transformations. Eigenvalues have numerous applications in physics, engineering, and computer science, including the study of vibrations, stability analysis, and data compression. The term is often used in conjunction with eigenvector, which is a non-zero vector that, when a linear transformation is applied to it, results in the vector being scaled by the eigenvalue. Understanding eigenvalues is crucial for solving systems of differential equations and for analyzing the behavior of complex systems.
nounA scalar value associated with a linear transformation, such that there exists a non-zero vector (an eigenvector) that, when the transformation is applied to it, results in the vector being scaled by that scalar value.
- A scalar value associated with a linear transformation.
- A value that represents how much change occurs in a linear transformation.
"The eigenvalues of the matrix represent the amounts by which the eigenvectors are scaled during the transformation."
"The eigenvalues of the matrix represent the amounts by which the eigenvectors are scaled during the transformation."
"The researcher calculated the eigenvalues to understand the stability of the system."
The plural form is used when referring to multiple eigenvalues.
"The researcher calculated the eigenvalues to understand the stability of the system."
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of eigenvalue
The term 'eigenvalue' originates from the German words 'eigen,' meaning 'own' or 'proper,' and 'value.' It was introduced by the German mathematician David Hilbert in the early 20th century. The concept of eigenvalues has its roots in the work of 18th-century mathematicians such as Leonhard Euler and Joseph-Louis Lagrange.
Usage notes
Formal and technical term used primarily in mathematics, physics, and engineering.