The crater Krylov on the Moon is named after him, as are the Krylov Peninsula and the Krylov State Research Center (a shipbuilding research institute of which Krylov had been superintendent).
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In 1931 he published a paper on what is now called the Krylov subspace and Krylov subspace methods.
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Krylov also published the first Russian translation of Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1915).
Ivan Krylov | Aleksey Nikolayevich Tolstoy | Aleksey Konstantinovich Tolstoy | Aleksey Semyonovich Vishnyakov | Aleksey Kuropatkin | Aleksey Khomyakov | Aleksey Burago | Krylov subspace | Krylov Peninsula | Drevin's sculpture of Ivan Krylov | Aleksey Yakimenko | Aleksey Trubetskoy | Aleksey Remizov | Aleksey Petrovich Yermolov | Aleksey Mikhaylovich Mikhalyov | Aleksey Kudryavtsev | Aleksey Krupnyakov | Aleksey Akatyev |