Convergence of products of matrices in projective spaces
نویسنده
چکیده
Let Ak, k ∈ N be a sequence of n×n complex valued matrices which converge to a matrix A. If A and each Ak is positive then the product AkAk−1...A2A1 ||AkAk−1...A2A1|| converges to a rank one matrix positive matrix uw, where u is a positive column eigenvector of A. If each Ak is nonsingular and A has exactly one simple eigenvalue λ of the maximal modulus with the corresponding eigenvector u, then e −1θk AkAk−1...A2A1 ||AkAk−1...A2A1|| , θk ∈ R converges to a rank one matrix uw. 2000 Mathematical Subject Classification: 15A48, 47H09, 65L20
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