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Eigenvalue Calculator

Calculate numerical eigenvalues of a 2×2 or 3×3 real square matrix, including complex roots.

Inputs

Matrix size

2 × 2 matrix

Row 1, column 1Row 1, column 2Row 2, column 1Row 2, column 2

3 × 3 matrix

Row 1, column 1Row 1, column 2Row 1, column 3Row 2, column 1Row 2, column 2Row 2, column 3Row 3, column 1Row 3, column 2Row 3, column 3

Result

Initializing.

Method and worked example

For 2×2 matrices the characteristic quadratic uses trace and determinant. For 3×3 matrices, coefficients come from trace, trace(A²), and determinant; a deterministic depressed-cubic routine returns all three numerical roots and verifies polynomial residuals.

Scope and limitations

2×2 and 3×3 real-entry matrices only. Numerical eigenvalues may have small rounding error. Eigenvectors, symbolic roots, arbitrary dimensions, RREF, and other general matrix operations are outside scope.

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