Types of Eigenvector
The eigenvectors calculated for the square matrix are of two types which are,
- Right Eigenvector
- Left Eigenvector
Right Eigenvector
The eigenvector which is multiplied by the given square matrix from the right-hand side is called the right eigenvector. It is calculated by using the following equation,
AVR = λVR
Where,
- A is given square matrix of order n×n,
- λ is one of the eigenvalues, and
- VR is the column vector matrix
The value of VR is,
[Tex]\bold{V_{R} = \begin{bmatrix} v_{1}\\ v_{2}\\ v_{3}\\ .\\ .\\ v_{n}\\ \end{bmatrix}}[/Tex]
Left Eigenvector
The eigenvector which is multiplied by the given square matrix from the left-hand side is called the left eigenvector. It is calculated by using the following equation,
VLA = VLλ
Where,
- A is given square matrix of order n×n,
- λ is one of the eigenvalues, and
- VL is the row vector matrix.
The value of VL is,
VL = [v1, v2, v3,…, vn]
Eigenvalues
Eigenvalues and Eigenvectors are the scalar and vector quantities associated with Matrix used for linear transformation. The vector that does not change even after applying transformations is called the Eigenvector and the scalar value attached to Eigenvectors is called Eigenvalues. Eigenvectors are the vectors that are associated with a set of linear equations. For a matrix, eigenvectors are also called characteristic vectors, and we can find the eigenvector of only square matrices. Eigenvectors are very useful in solving various problems of matrices and differential equations.
In this article, we will learn about eigenvalues, eigenvectors for matrices, and others with examples.
Table of Content
- What are Eigenvalues?
- What are Eigenvectors?
- Eigenvector Equation
- What are Eigenvalues and Eigenvectors?
- How to Find an Eigenvector?
- Types of Eigenvector
- Right Eigenvector
- Left Eigenvector
- Eigenvectors of a Square Matrix
- Eigenvector of a 2 × 2 matrix
- Eigenvector of a 3 × 3 Matrix
- Eigenspace
- Appliactions of Eigen Values
- Diagonalize Matrix Using Eigenvalues and Eigenvectors
- Solved Examples on Eigenvectors
- FAQs on Eigenvectors