Eigenvalue calculator
Type a square matrix, one row per line, and get its eigenvalues and eigenvectors. Complex eigenvalues are shown as a + bi.
One row per line, numbers separated by spaces. Fractions such as 1/2 are allowed.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
What are eigenvalues?
An eigenvector v of a matrix A is a vector that A only stretches or shrinks, without changing its direction: Av = λv. The factor λ is the eigenvalue. The eigenvalues are the solutions of det(A − λI) = 0.
Checks
The sum of the eigenvalues equals the trace (the sum of the diagonal), and their product equals the determinant. The eigenvectors are scaled so that the smallest component is 1; any multiple of an eigenvector is also an eigenvector.
Where they are used
In vibrations and stability analysis, in Google's original PageRank, in principal component analysis (PCA) and in quantum mechanics. The calculation is numerical, done by math.js in your browser, for matrices up to 8×8.
Frequently asked questions
Is the eigenvalue calculator free?
Yes. The eigenvalue calculator is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.