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Eigenvalue Calculator

Calculate and check eigenpairs for a real symmetric matrix. See normalized eigenvectors and the residual for each result.

Enter 2–8 rows, one per line. Separate values with commas, spaces or semicolons. Example: 2, 0 on the first line and 0, 3 on the second.

Supports finite real symmetric matrices only, from 2×2 to 8×8; each value must be within ±1,000,000. Non-symmetric matrices and complex eigenvalues are not supported. Eigenvectors have unit length; their sign may vary. Floating-point results are approximate.

How do I find the eigenvalues of a matrix?

Enter a square real symmetric matrix, one row per line, with values separated by commas or spaces. Calculate to view sorted eigenvalues, normalized eigenvectors and residuals.

Frequently asked questions

How do I find the eigenvalues of a matrix?

Enter a square real symmetric matrix, one row per line, with values separated by commas or spaces. Calculate to view sorted eigenvalues, normalized eigenvectors and residuals.

Are my matrix values uploaded?

No. The calculation runs locally in this browser. Matrix values are not uploaded or saved by this tool.

What matrix types does this eigenvalue calculator support?

It supports real symmetric square matrices from 2×2 through 8×8. It does not calculate eigenvalues for non-symmetric matrices or complex eigenvalues.

How can I check an eigenvector?

For each result, compare A multiplied by the displayed normalized vector with the eigenvalue multiplied by that vector. The residual reports the norm of their difference; values near zero indicate a close numerical match.

Why can an eigenvector have a different sign?

If v is an eigenvector, −v is also an eigenvector for the same eigenvalue. The tool chooses a consistent sign where possible, but sign is not mathematically unique.