Enter the size of the matrix and its elements to calculate the eigenvectors using the calculator.
Eigenvector Calculation Formula
The following formula is used to calculate the eigenvectors of a matrix:
Av = λv
Variables:
- A is the square matrix
- v is the eigenvector
- λ is the eigenvalue
To calculate the eigenvectors, solve the equation Av = λv for v given matrix A and eigenvalue λ.
What is Eigenvector Calculation?
Eigenvector calculation involves determining vectors that, when multiplied by a matrix, yield a scalar multiple of themselves. This process is critical in various fields including physics, engineering, and computer science, especially for problems involving linear transformations and stability analysis.
How to Calculate Eigenvectors?
The following steps outline how to calculate eigenvectors:
- Input the matrix size and its elements.
- Determine the eigenvalues for the matrix.
- Solve the equation Av = λv to find the eigenvectors.
- Verify your results with the calculator provided.
Example Problem:
Use the following matrix as an example problem:
Matrix A = [[2, 1], [1, 2]]
Calculate the eigenvectors of this matrix.
FAQ
1. What is an eigenvector?
An eigenvector is a non-zero vector that changes only in scale when a linear transformation is applied, corresponding to a specific eigenvalue.
2. How are eigenvectors used?
Eigenvectors are used in various applications such as solving differential equations, stability analysis, and in algorithms for dimensionality reduction in machine learning.
3. Can I calculate eigenvectors for any matrix?
Eigenvectors can be calculated for square matrices. For non-square matrices, other methods such as singular value decomposition (SVD) are used.