Interactive Eigenvector Calculator
Calculate and visualize eigenvectors of a square matrix with interactive plots. Understand linear transformations visually.
Enter Matrix
Input a square matrix in JSON format. For example: [[1, 2], [3, 4]].
Eigenvalues:
Eigenvectors:
Eigenvector Visualization
Understanding Eigenvectors
In linear algebra, an eigenvector of a square matrix is a non-zero vector that, when the matrix is multiplied by, yields a scalar multiple of itself. This scalar is called the eigenvalue associated with the eigenvector. In simpler terms, if you apply a linear transformation represented by a matrix to its eigenvector, the eigenvector only changes in scale, not in direction.
Eigenvectors and eigenvalues are fundamental concepts with applications in various fields like physics, engineering, and data science. For instance, in principal component analysis (PCA), eigenvectors of the covariance matrix are used to identify the principal components, which are directions of maximum variance in the data.
How to Use This Calculator
- Enter your square matrix in the JSON format in the input box. For example,
[[4, 2], [1, 3]]for a 2x2 matrix. - Click the "Calculate Eigenvectors" button to compute the eigenvectors and eigenvalues.
- The results will be displayed below, and an interactive visualization will appear if the calculation is successful.
- Use the "Copy" buttons to easily copy the eigenvalues and eigenvectors to your clipboard.
- Click "Reset" to clear the input and outputs.
Learn more about eigenvectors on Wikipedia.