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Singular Values Calculator

With this singular values calculator, you'll quickly and easily learn how to find singular values of any matrix.

One row per line, values separated by commas or spaces.
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Eigenvalues8.87298335, 1.12701665all real
Trace10equals the sum of the eigenvalues
Determinant10equals the product of the eigenvalues
Rank2
Sum of eigenvalues10
Product of eigenvalues10

Your matrix

47
26

The method

solve det(A − λI) = 0 for the eigenvalues λ

What an eigenvalue is

An eigenvector is a direction the matrix does not turn — it only stretches it. The eigenvalue is how much: Av = λv. Complex eigenvalues mean no real direction survives unturned, which is the signature of a rotation.

Two useful checks: the eigenvalues always sum to the trace and multiply to the determinant. Both are shown above.