Suppose I have an n x n matrix and I want to find the dominant eigenvalue and its associated eigenvector. Given these dimensions, what is the minimum number of iterations of the power iteration method that I should use to cause the values to converge in such a fashion that the ranks of the matrix will be accurate? (I.e., I want every element of the eigenvector to be < or > other elements of the eigenvector correctly.)
2026-04-01 01:34:57.1775007297
How many iterations are generally required when using the power iteration method?
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The elements in the leading eigenvector can be arbitrarily close to zero and I believe this means that in arbitrary powers of the matrix, you may get that the apparent leading eigenvector of the power matrix (i.e. the entries in the matrix raised to a power applied to an arbitrary non-zero vector) have entries out of order with respect to the order of the entries of the true leading eigenvector of the matrix.