Power Iteration Simulator

Estimate a dominant eigenvalue and eigenvector by repeated matrix multiplication

Iterations

Power Iteration Formula

Multiply	w_k = A v_k
Normalize	v_{k+1} = w_k / \|\|w_k\|\|
Estimate eigenvalue	lambda approx v^T A v / v^T v

How to Read the Simulator

Each step multiplies the current vector by the matrix.
The vector is normalized to keep the direction stable.
If the method converges, the vector approaches a dominant eigenvector.
The Rayleigh quotient estimates the corresponding eigenvalue.

Frequently Asked Questions

What is power iteration?▼

Power iteration is an iterative method for estimating the dominant eigenvalue and eigenvector of a matrix.

What is a dominant eigenvalue?▼

The dominant eigenvalue is the eigenvalue with the largest absolute value.

Why normalize the vector?▼

Normalization prevents the vector from growing too large or too small while preserving its direction.

When can power iteration fail?▼

It can converge slowly or fail when there is no clearly dominant eigenvalue or when the starting vector is poorly aligned.

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