EIGENVECTOR Meaning and
Definition
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An Eigenvector, also known as a characteristic vector, represents a distinct direction within a vector space. Specifically, it refers to a non-zero vector that remains collinear but may be scaled by a scalar value when a linear transformation is applied. In other words, multiplying a matrix by its corresponding eigenvector results in the same vectors, merely stretching or shrinking them.
The concept of eigenvectors is primarily employed in linear algebra, where they play a crucial role in a variety of applications. For instance, in physics, eigenvectors are utilized to determine the principal axes of an object's rotation or vibration. In mathematics, they represent the directions that remain unchanged when a linear transformation is applied and are foundational in solving systems of differential equations.
To calculate eigenvectors of a square matrix, one needs to solve the following equation: Ax = λx, where A represents the matrix, x denotes the eigenvector, and λ stands for the eigenvalue associated with that eigenvector. The eigenvalue is the scalar by which the eigenvector is scaled during the transformation. By solving this equation, eigenvalues and eigenvectors can be determined, allowing for further analysis and understanding of the transformation's impact on the vector space.
In summary, an eigenvector is a non-zero vector within a vector space that remains collinear but may be scaled when a linear transformation is applied. The eigenvector-concept is extensively used in various fields, such as physics and mathematics, as it helps in comprehending and analyzing linear transformations and their effects on a given vector space.
Common Misspellings for EIGENVECTOR
- wigenvector
- sigenvector
- digenvector
- rigenvector
- 4igenvector
- 3igenvector
- eugenvector
- ejgenvector
- ekgenvector
- eogenvector
- e9genvector
- e8genvector
- eifenvector
- eivenvector
- eibenvector
- eihenvector
- eiyenvector
- eitenvector
- eigwnvector
- eigsnvector
Etymology of EIGENVECTOR
The word "eigenvector" is derived from the German word "Eigenvektor". "Eigen" means "own" or "characteristic", and "vektor" translates to "vector" in English. The term was coined by the German mathematician David Hilbert in the early 20th century to describe a specific type of vector associated with linear transformations and matrices. The word "eigenvector" was later adopted by the English-speaking mathematical community and is now commonly used worldwide.
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