V knige izlagaetsya universal'nyy metod resheniya zadach lineynoy algebry metod elementarnykh preobrazovaniy matrits. Na mnogochislennykh primerakh pokazano, kak reshayutsya osnovnye zadachi lineynoy algebry: reshenie sistem lineynykh uravneniy, vychislenie obratnoy matritsy, lineynaya zavisimost' i lineynaya obolochka sistemy vektorov, nakhozhdenie sobstvennykh chisel i sobstvennykh vektorov lineynogo operatora, yadro i obraz lineynogo operatora, privedenie polinomial'noy matritsy k kanonicheskomu vidu, nakhozhdenie zhordanovoy i frobeniusovoy form matritsy, privedenie kvadratichnoy formy k summe kvadratov, razlichnye vidy razlozheniya matrits, nakhozhdenie ortogonal'nogo bazisa podprostranstva, natyanutogo na dannuyu sistemu vektorov, i t.d. Kniga prednaznachena kak dlya studentov, izuchayushchikh lineynuyu algebru v ob"eme universitetskogo kursa, tak i dlya prepodavateley, provodyashchikh prakticheskie zanyatiya po etomu predmetu.
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