The Eigenvalue Calculator finds the eigenvalues and eigenvectors of square matrices. Eigenvalues and eigenvectors are fundamental concepts in linear algebra, used in physics, engineering, computer science, and data analysis.
Enter a square matrix (2x2 or 3x3) and the calculator will compute all eigenvalues and their corresponding eigenvectors.
Enter the 2\u00d72 matrix elements:
Your calculations will appear here
An eigenvalue of a matrix A is a scalar lambda such that Av = lambda*v for some non-zero vector v (the eigenvector). This means the matrix transformation only scales the vector without changing its direction.
Eigenvalues are found by solving the characteristic equation det(A - lambda*I) = 0. For a 2x2 matrix, this gives a quadratic equation; for 3x3, a cubic equation.
Problem: Find the eigenvalues of [[4, 1], [2, 3]]
Solution: Characteristic equation: (4-lambda)(3-lambda) - 2 = lambda^2 - 7*lambda + 10 = 0
Answer: lambda = 5 and lambda = 2
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