How this calculation works
Find the largest absolute eigenvalue, which controls powers of a symmetric matrix.
THE FORMULA
Eigenvalues = (a+d)/2 ± hypot((a−d)/2,b)A worked example
The matrix with diagonal 3 and off-diagonal 1 has eigenvalues 4 and 2, so its spectral radius is 4.
Good to know
The shortcut assumes a real symmetric matrix.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Find the largest absolute eigenvalue, which controls powers of a symmetric matrix.
The primary result is labeled “Spectral radius”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The shortcut assumes a real symmetric matrix.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The matrix with diagonal 3 and off-diagonal 1 has eigenvalues 4 and 2, so its spectral radius is 4.
Which rule does this calculator apply?
Eigenvalues = (a+d)/2 ± hypot((a−d)/2,b)