What does eigenvector mean?
An eigenvector is a non-zero vector that, when a linear transformation is applied to it, results in a scaled version of itself. The scalar that multiplies the eigenvector is called the eigenvalue. Eigenvectors are used to study the properties of linear transformations and matrices, and have numerous applications in physics, engineering, and computer science. They are a fundamental concept in linear algebra and are used to diagonalize matrices, solve systems of differential equations, and analyze the stability of systems. Understanding eigenvectors is crucial for working with linear transformations and matrices.
nounA non-zero vector that, when a linear transformation is applied to it, results in a scaled version of itself.
- A vector that is scaled by a linear transformation.
- A direction that remains unchanged under a linear transformation.
"The eigenvector of a matrix represents a direction that is unchanged under the transformation represented by the matrix."
"The eigenvectors of a matrix are used to diagonalize the matrix."
"The direction of the eigenvector is an invariant under the transformation."
The plural form is used when referring to multiple eigenvectors.
"The eigenvectors of the matrix are used to diagonalize it."
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of eigenvector
The term 'eigenvector' comes from the German word 'eigen', meaning 'own' or 'proper', and the English word 'vector'. It was coined by the German mathematician David Hilbert in the early 20th century. The concept of eigenvectors and eigenvalues was first developed by the French mathematician Auguste Cauchy in the 19th century.
Usage notes
Typically used in the context of linear algebra and matrix theory.