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Fj(\()p Fi(B)5 b Fj(\))32 b(ein)h(Isomorphism)m(us)f(in)f Fg(D)36 b Fj(ist.)70 3611 y(12.)49 b(Sei)d Fl(Mat)h Fj(die)f(Kategorie)g(b)s (estehend)i(aus)f(Ob\()p Fl(Mat)q Fj(\))k(=)h Fa(N)2612 3626 y Fc(0)2657 3611 y Fj(,)47 b(der)g(Menge)g(der)g(nat)3564 3615 y(\177)3561 3611 y(urlic)m(hen)244 3731 y(Zahlen)c Fg(\025)k Fj(0,)d(und)g(Mor)1202 3765 y Fl(Mat)1410 3731 y Fj(\()p Fi(m;)17 b(n)p Fj(\))47 b(:=)g Fa(R)1936 3695 y Fc(\()q Fh(m;n)p Fc(\))2126 3731 y Fj(,)d(der)g(Menge)h(der)f (reellen)g(Matrizen)g(mit)e Fi(m)244 3852 y Fj(Zeilen)31 b(und)i Fi(n)g Fj(Spalten.)285 4055 y(\(a\))48 b(Zeige)39 b(Sie,)f(dass)i Fl(Mat)g Fj(mit)d(der)i(Matrizenm)m(ultiplik)-5 b(ation)34 b(eine)39 b(Kategorie)f(bildet.)g(\(Be-)458 4175 y(ac)m(h)m(ten)c(Sie)f(b)s(esonders)h(das)f(Ob)5 b(jekt)33 b(0)28 b Fg(2)g Fa(N)2114 4190 y Fc(0)2159 4175 y Fj(.\))280 4337 y(\(b\))48 b(Konstruieren)29 b(Sie)f(einen)g(F) -8 b(unktor)28 b(v)m(on)h Fl(Mat)g Fj(in)e(die)h(Kategorie)f(der)h (endlic)m(hdimensiona-)458 4458 y(len)k(reellen)f(V)-8 b(ektorr)1245 4462 y(\177)1245 4458 y(aume)32 b Fl(V)-9 b(ek)1690 4473 y Fh(ed)1795 4458 y Fj(un)m(ter)33 b(V)-8 b(erw)m(endung)34 b(der)e(durc)m(h)h(Matrizen)e(dargestell-)458 4578 y(ten)i(linearen)f(Abbildungen.)290 4740 y(\(c\))49 b(*)33 b(Konstruieren)g(Sie)f(einen)g(F)-8 b(unktor)33 b(v)m(on)g Fl(V)-9 b(ek)2280 4755 y Fh(ed)2386 4740 y Fj(nac)m(h)33 b Fl(Mat)p Fj(.)0 5172 y(Abgab)s(e:)g(F)-8 b(reitag,)31 b(14.5.2004,)g(15)h(Uhr,)h(in)f(der)h(V)-8 b(orlesung.)0 5292 y(Bitte)32 b(geb)s(en)h(Sie)f(auf)g(Ihrer)i(L)1152 5296 y(\177)1152 5292 y(osung)e(Ihren)i(Namen)e(an.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF