Linear Algebra Rank of a Matrix Problem: Prove that a(k) array is monotonically increasing

Heeyeyey

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Let A be a n x n matrix with complex elements. Prove that the a(k) array, with k ∈ ℕ, where a(k) = rank(A^(k + 1)) - rank(A^k), is monotonically increasing.
 

Heeyeyey

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Mar 5, 2019
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Let A be a n x n matrix with complex elements. Prove that the a(k) array, with k ∈ ℕ, where a(k) = rank(A^(k + 1)) - rank(A^k), is monotonically increasing.

Sorry for reposting this here, but I was not 100% sure where I should post it and I really need a solution for this problem as I have tried to solve it quite a lot. Thank you!
 

Heeyeyey

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Mar 5, 2019
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Finally solved it using the Frobenius Inequality for the rank of a matrix. Thank you anyway!
 
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