Compute eigenvalues of square matrices with step-by-step explanations.
100% Free2×2, 3×3, largerWith Steps
Matrix Configuration
Set the matrix size (square matrices only for eigenvalues)
3×3
Matrix Input
Enter matrix elements (decimals and fractions allowed)
Example Matrices
Click on any example to load it into the calculator
2×2 Basic Example
Simple 2×2 matrix with real eigenvalues
[2, 1]
[1, 3]
3×3 Example
3×3 matrix with mixed eigenvalues
[1, 2, 3]
[3, 2, 1]
[2, 1, 3]
Identity Matrix
3×3 identity matrix (eigenvalues = 1)
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Symmetric Matrix
Symmetric matrix with real eigenvalues
[4, 1, 2]
[1, 3, 0]
[2, 0, 5]
Frequently Asked Questions
Eigenvalues are special scalars λ that satisfy the equation Av = λv for a matrix A and non-zero vector v (called an eigenvector). They reveal intrinsic properties of linear transformations, showing how the matrix scales vectors along certain directions. Eigenvalues are fundamental in physics (vibrational modes, quantum mechanics), engineering (stability analysis), and data science (PCA, machine learning).