##  [Krylov Subspace](/krylov-subspace) 

  ##  [Krylov Subspace](https://natural.quantumdictionary.io/krylov-subspace-0) 

  

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Definition

Given a matrix A and a vector b, the m-th Krylov subspace is span{b, A b, A^2 b, ..., A^{m-1} b}. It is the minimal A-invariant subspace reachable from b by polynomial action of A up to degree m-1.