588 KB23 KB201420242023Ravnikar, Christianštevilka:1letnik:108 str.COBISSID_HOST:150987011ISSN:2385-8567URN:URN:NBN:SI:doc-VOEJDI7RslZaložba Fakultete za matematiko in fiziko Univerze v LjubljaniMatrikacomplex coefficientskompleksni koeficientiničlepolinomipolynomialsroots of polynomialsNičle polinomov so zvezno odvisne od koeficientov polinomov|Every polynomial of degree ?$n$? with complex coefficients has exactly ?$n$? roots (counting their multiplicity). Intuitively, it seems to be the case that if the coefficients of a polynomial are slightly altered, their roots will also differ by just a little. It is not entirely obvious, however, how one would prove that, since there is no explicit formula for roots of polynomials of degree four or more. It is also Not obvious, how one would define nearness on a set of roots, which would consider that by changing the coefficients, their multiplicity may also changeVsak polinom stopnje ?$n$? s kompleksnimi koeficienti ima (ob upoštevanju večkratnosti) natanko ?$n$? ničel. Intuitivno se zdi, da se ob majhni spremembi koeficientov polinoma tudi njegove ničle le malo spremenijo. Ni pa povsem očitno, kako bi to dokazali, saj za polinome stopnje večje od štiri nimamo eksplicitne formule za ničle. Prav tako ni očitno, kako definirati pojem bližine na množici ničel, ki bo upošteval, da se ob spreminjanju koeficientov lahko spremeni tudi večkratnost ničelTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of Slovenia