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Eigenvalues & Eigenvectors (2x2, 3x3) — with steps

Walk learners through characteristic polynomials, rational-root checks, QR iteration, eigenvectors, residuals, and diagonalizability with shareable outputs.

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Inputs

2x2 visualization (grid, eigenvectors, power iteration)

Result

How it's calculated

    Teacher notes

    FAQ

    Can I export the steps or share the setup?

    Use Alt+S (or the Share button) to copy a URL with all inputs encoded. Alt+L copies a LaTeX summary of the characteristic polynomial for worksheets or LMS uploads.

    What happens with repeated or defective eigenvalues?

    The tool compares algebraic and geometric multiplicities. If the geometric multiplicity is smaller, the diagonalizability badge switches to “No” and residuals highlight the defective eigenspace.