Loterre: Mathematics: Krylov subspace

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Krylov subspace

In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A (starting from ${\\displaystyle A^{0}=I}$ ), that is,

${\\displaystyle {\\mathcal {K}}_{r}(A,b)=\\operatorname {span} \\,\\{b,Ab,A^{2}b,\\ldots ,A^{r-1}b\\}.}$

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