How this calculation works
Estimate an eigenvalue with normalized power iteration and report the final eigenpair residual.
Start at (1,1)/√2, repeatedly normalize Ax, then compute xᵀAxA worked example
The vector (1,1) is already an eigenvector of [[3,1],[1,3]] with eigenvalue 4.
Good to know
The seed must have a component along the dominant eigenspace for convergence to that eigenvalue.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Estimate an eigenvalue with normalized power iteration and report the final eigenpair residual.
The primary result is labeled “Rayleigh estimate”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The seed must have a component along the dominant eigenspace for convergence to that eigenvalue.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The vector (1,1) is already an eigenvector of [[3,1],[1,3]] with eigenvalue 4.
Which rule does this calculator apply?
Start at (1,1)/√2, repeatedly normalize Ax, then compute xᵀAx