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222 758 y Fg(1.)h(Betrac)o(h)o(ten)14 b(Sie)i(die)g(Matrix)821
914 y Ff(A)d Fg(=)923 814 y Fe(0)923 904 y(@)967 854
y Fg(1)61 b(2)80 b(1)967 914 y(2)61 b(1)g Fd(\000)p Fg(2)967
974 y(1)41 b Fd(\000)p Fg(2)61 b(1)1200 814 y Fe(1)1200
904 y(A)284 1081 y Fg(mit)17 b(reellen)g(Ein)o(tr)644
1083 y(\177)644 1081 y(agen.)i(Bestimm)o(en)d(Sie)i(eine)g(orthogonale)
i(Matrix)f Ff(O)q Fg(,)g(f)1736 1083 y(\177)1735 1081
y(ur)284 1141 y(die)c Ff(O)400 1123 y Fc(T)429 1141 y
Ff(AO)i Fg(eine)e(Diagonalmatrix)h(ist.)684 b(\(5\))222
1243 y(2.)24 b(Geb)q(en)18 b(Sie)g(die)g(Matrizen)f Ff(D)850
1250 y Fc(x)891 1243 y Fg(und)i Ff(D)1031 1250 y Fc(y)1071
1243 y Fg(an,)f(die)g(im)f Fb(R)1347 1225 y Fa(3)1382
1243 y Fg(die)h(Dreh)o(ung)g(um)1754 1223 y Fc(\031)p
1754 1231 22 2 v 1756 1260 a Fa(6)284 1303 y Fg(um)h(die)h(x-Ac)o(hse)f
(bzw.)h(die)f(y-Ac)o(hse)h(b)q(esc)o(hreib)q(en.)f(Geb)q(en)h(Sie)g
(die)g(Matrix)284 1363 y(an,)13 b(die)f(die)g(Komp)q(osition)h(der)f(b)
q(eiden)h(Dreh)o(ungen)g(b)q(esc)o(hreibt,)e(w)o(ob)q(ei)i(zuerst)284
1423 y(um)f(die)h(x-Ac)o(hse)f(und)i(dann)g(um)f(die)g(y-Ac)o(hse)f
(gedreh)o(t)h(wird.)g(Bestimm)o(en)d(Sie)284 1483 y(die)15
b(Drehac)o(hse)h(der)g(Komp)q(osition.)751 b(\(5\))222
1585 y(3.)24 b(Betrac)o(h)o(ten)14 b(Sie)i(die)g(Abbildung)653
1695 y Fb(R)692 1675 y Fa(2)723 1695 y Fd(!)d Fb(R)p
Ff(;)8 b Fg(\()p Ff(x)894 1702 y Fa(1)911 1695 y Ff(;)g(x)961
1702 y Fa(2)980 1695 y Fg(\))14 b Fd(7!)f Ff(x)1104 1675
y Fa(2)1104 1707 y(1)1135 1695 y Fd(\000)e Fg(5)p Ff(x)1237
1702 y Fa(1)1256 1695 y Ff(x)1284 1702 y Fa(2)1315 1695
y Fg(+)g Ff(x)1392 1675 y Fa(2)1392 1707 y(2)284 1805
y Fg(Bestimm)o(en)i(Sie)j(eine)f(orthogonale)j(Matrix)861
1941 y Ff(A)13 b Fg(=)963 1871 y Fe(\022)1000 1911 y
Ff(a)1026 1918 y Fa(11)1104 1911 y Ff(a)1130 1918 y Fa(12)1000
1971 y Ff(a)1026 1978 y Fa(21)1104 1971 y Ff(a)1130 1978
y Fa(22)1167 1871 y Fe(\023)284 2078 y Fg(so)k(da\031)g(f)452
2080 y(\177)451 2078 y(ur)f Ff(y)537 2085 y Fa(1)570
2078 y Fg(=)e Ff(a)648 2085 y Fa(11)685 2078 y Ff(x)713
2085 y Fa(1)744 2078 y Fg(+)d Ff(a)819 2085 y Fa(12)856
2078 y Ff(x)884 2085 y Fa(2)919 2078 y Fg(und)17 b Ff(y)1041
2085 y Fa(2)1074 2078 y Fg(=)d Ff(a)1152 2085 y Fa(21)1189
2078 y Ff(x)1217 2085 y Fa(1)1247 2078 y Fg(+)d Ff(a)1322
2085 y Fa(22)1359 2078 y Ff(x)1387 2085 y Fa(2)1423 2078
y Fg(gilt:)722 2207 y Ff(x)750 2187 y Fa(2)750 2219 y(1)780
2207 y Fd(\000)g Fg(5)p Ff(x)882 2214 y Fa(1)902 2207
y Ff(x)930 2214 y Fa(2)961 2207 y Fg(+)g Ff(x)1038 2187
y Fa(2)1038 2219 y(2)1071 2207 y Fg(=)1128 2173 y(7)p
1128 2196 25 2 v 1128 2241 a(2)1157 2207 y Ff(y)1183
2187 y Fa(2)1181 2219 y(1)1213 2207 y Fd(\000)1268 2173
y Fg(3)p 1268 2196 V 1268 2241 a(2)1297 2207 y Ff(y)1323
2187 y Fa(2)1321 2219 y(2)1718 2333 y Fg(\(4\))222 2434
y(4.)24 b(Sei)15 b Ff(A)e Fd(2)h Ff(GL)p Fg(\()p Ff(n;)8
b Fb(R)p Fg(\))14 b(eine)h(in)o(v)o(ertierbare)e(Matrix)i(mit)f
(reellen)g(Ein)o(tr)1573 2436 y(\177)1573 2434 y(agen.)i(Zei-)284
2495 y(gen)d(Sie,)f(da\031)i(sic)o(h)e Ff(A)h Fg(als)g(Pro)q(dukt)h
Ff(A)f Fg(=)h Ff(O)q(D)q(N)20 b Fg(sc)o(hreib)q(en)12
b(l)1416 2497 y(\177)1416 2495 y(a\031t,)h(w)o(ob)q(ei)g
Ff(O)i Fg(eine)p eop
%%Page: 2 2
2 1 bop 284 274 a Fg(orthogonale)13 b(Matrix,)d Ff(D)j
Fg(eine)e(Diagonalmatrix)g(mit)e(p)q(ositiv)o(en)i(Ein)o(tr)1606
276 y(\177)1606 274 y(agen)g(auf)284 334 y(der)18 b(Diagonalen,)h(und)f
Ff(N)24 b Fg(eine)17 b(ob)q(ere)i(Dreiec)o(ksmatrix)c(mit)h(Einsen)i
(auf)h(der)284 394 y(Diagonalen)e(ist.)284 475 y(\(Hin)o(w)o(eis:)h(W)l
(enden)i(Sie)f(das)i(Orthonormalisierungsv)o(erfahren)e(v)o(on)h(Gram-)
284 535 y(Sc)o(hmidt)13 b(auf)i(die)g(Spalten)o(v)o(ektoren)e(v)o(on)i
Ff(A)g Fg(an.)g(Dab)q(ei)g(en)o(tsteh)o(t)f(eine)g(Ortho-)284
596 y(normalbasis,)f(die)h(aus)h(den)f(Spalten)g(der)g(b)q(en)1149
598 y(\177)1149 596 y(otigten)g(Matrix)g Ff(O)i Fg(b)q(esteh)o(t.)d
(Die)284 656 y(Diagonalmatrix)h(en)o(tspric)o(h)o(t)e(dem)h
(Normierungssc)o(hritt)g(im)f(Gram-Sc)o(hmidt-)284 716
y(V)l(erfahren.)17 b(Die)h(ob)q(ere)h(Dreiec)o(ksmatrix)c(en)o(tspric)o
(h)o(t)i(den)h(Ko)q(e\016zien)o(ten,)e(die)284 776 y(b)q(eim)412
766 y(\177)406 776 y(Ub)q(ergang)j(v)o(on)e(der)h(einen)f(zur)g
(anderen)h(Basis)g(auftreten.)f(Diese)g(Zer-)284 836
y(legung)f(wird)g(als)h(Iw)o(asa)o(w)o(a-Zerlegung)f(b)q(ezeic)o
(hnet.\))421 b(\(6\))162 951 y(Abgab)q(e:)20 b(Mitt)o(w)o(o)q(c)o(h,)e
(4.7.2001,)i(9.00)g(Uhr,)1027 940 y(\177)1021 951 y(Ubungsk)1208
953 y(\177)1208 951 y(asten)g(im)e(1.)h(Sto)q(c)o(k)h(des)f(Ma-)162
1011 y(thematisc)o(hen)14 b(Instituts.)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF