From f4c36cb12910467bc75b2e19d99fa0090c9a9b4e Mon Sep 17 00:00:00 2001 From: flavis Date: Wed, 20 May 2020 12:11:34 +0200 Subject: [PATCH] fix double fullstop and add support for more relation symbols in salign --- ana8.tex | 4 ++-- analysisII.pdf | Bin 522643 -> 522643 bytes lecture.cls | 11 +++++++++-- 3 files changed, 11 insertions(+), 4 deletions(-) diff --git a/ana8.tex b/ana8.tex index ff99995..8c3996a 100644 --- a/ana8.tex +++ b/ana8.tex @@ -15,7 +15,7 @@ \begin{proof} Sei $x \in \mathbb{K}^{n}$. Dann ist - \begin{salign} + \begin{salign*} \Vert (\mathbb{I} + B) x \Vert &= \Vert x + B x\Vert \\ &\stackrel{\text{Dreiecksungl.}}{\ge } \Vert x \Vert - \Vert Bx \Vert \\ @@ -33,7 +33,7 @@ - \Vert B (\mathbb{I} + B)^{-1} \Vert \\ &\ge \Vert (\mathbb{I} + B)^{-1} \Vert - \Vert B \Vert \cdot \Vert (\mathbb{I} + B)^{-1} \Vert \\ &= (1 - \Vert B \Vert) \Vert (\mathbb{I} + B)^{-1} \Vert - .\end{salign} + .\end{salign*} Damit folgt die Behauptung. \end{proof} diff --git a/analysisII.pdf b/analysisII.pdf index ece0cdf613c8e00432b8f1d63b032a54770ff9fb..6c7d7e7c8f46f2e07efa77fa1237cf1a9efe77d9 100644 GIT binary patch delta 3983 zcmai$X*3j!+r}+1gPF08v5hSvW8boGV=K|jJd%AG$z;tMlEK(_Sw^84iAdSEEGa`# zAx0yz3{uuCP1d|U|Nnc=`|%(Q#Vs791{z$D)$ ze!|oZ#A9Xi${?6Vh*F4+cVquODCz|w4G1qCr8uztKLyi{N^xeC zIQU@lt&Ft}mgjPrx{vx)T-3C(P`o|Xf|m)nQfq>G!$qVl)jwRg;AAyBMNs7A*&5|3WNt%*Sqd56H zcnwgw#TdIjJD?LgU!8M`^LAf|w{*C(pl&&+E&a{!>ilolox;Iyvs@bcU2ixPR)jQ4 zA%$$8->#8Vyi21JzA#*J0?4+Um$~q2fpmeL-8+xMmOA{nlQ>R7qZshGq$Y`zv^zZ-({N~=I?_5&Yd&=W50%hL z@MXDLn@}P?^ofX2zBGNIA(oMU_}g*S29ldSD)=qt$j<}H$Eic5{eHssn2Sq##8ng{ zO*`C2huT}(7T)E_EY$MK>Q3D3Vup13-W!}F<@OJD<@yPw^2ZocoEAWE_LlO@spmhs zY-zok5|Ns8sg9Wjs*lch*WWGp*4<8emWcW*grf*w)M=?mGpy^W;=`sYSv}cf;p1HC zuXweO`G|V+=roT^&Ef|FSHL$oHP-FIg$<1}cLSJg8I)AZQW}r1R;(jN#tHiwP3jq8 zSv8iFkY7;l*DJRTx7{X>xPEg~g~-{fiPSOrmwpUBfv<=Wdf*01-egN(2ZLwG?XMEN zHfzUWJ}i<_O~t>WdJaOHy7mVKA;k;S_`vLIV!P}d6^_xUpi@q+%kABY4YNjyD z>Gq^Ax7sUtPSqBv&$^l$dne_U>~M|V4}yS1&gh)wb!zF$K0{ z(EAzR^GI8F<^BEA$k}%$^8CJ$=S9=oYS}4eQF{DVsoK}Vj57+Ex3CS3;eyGgdWGNJ zL@yz|4XhHS_y~9!is_Qcd0DVmnS4HB2gN97oR;1(L?@-?4E!WZu!yK9d>hSos)_s1 z!4?{4Ac^h5oyo`;oGE)CnIHQtdRR*e+dzd8BS;Y2xXab+*gyH!ZzjE%G8R-zf49a# zMn!c#p$T@1%`{blOwwo#TT7YdM4}%K=%8pv_r8OM;IDwnu5zv-71hfKf%%_=ggU4n zXX&P%vy(u_TQ_URKo1CaCwcr#B1Z?vbeCrDX%k%>C;U~9g-ktogI&M8I2}IclO49= zPj?kA11LBJ6-V@>pF~Y;uCa9gXc62?j2RU>_sR%%q)Yuka95_rgA+ZJMW}uGxhRH; zGA?sG!GFkJ0I)c<$>+#hium;eY{+&F$$fc&Uq|vDJa^U8K zl!3BH(2<3TJxOT+K}F`8DolLwRtVSdsT@Ap6OAR@0z%$!?{h|T%=MwQSO*u* zM03h4@EtQ4zP@rxC??5mqq~lBm^nPRz^TQ2n%Hy;@+V>UC(OCtd%8L-cer=q-Yq{B zSj=TA)pa;=l+c*_3jI-=>yWhM)R^)L zWz=(;M`ppgi3 z5U5|}e*x-D+PAz@_??9W175QX*`DgP2V4Y6sc=oA;Gd?h9~qB=fY#y(5^u;WD_=b6 zyM$0y3{2G}`lia7I4LfLRT3|hg8L7}3;K0A!`uo3uAmspxv6g09Ue<8Zj}~zrOgTG zD_#{>!pg(%_;R0)?-BL@Cund@8rd^@fZ=hfz|y#sq~~1~aIQV0Kk@9Ed|yze(o~S8 zpZH=q?62*;i5twYixP0IA+Dd5NBD33zmO6wz6{V#Tz#Ci&P{x*9~U2$rf7%IRAMI%<^j6W`pVBwbca z#*Yof>o`Ly3&7gWkn*dr)gbL6ySw#sRRr8r_N60f{T#cq_3Gd<%9#hjQ;+P_>fL5e za4oTg&h$#kzxnw$KHXNKQ5QL;BOAWo1N5eJIg*_G$GUsJkD>QUq;}?D-3EN!Z7BxR zW^?`|G3LEqGthTARyr?1uLMTu#q%NC1Hap-te;mo4pN~BsoX2(=$uxhI?S-?yzH+| zr8``EO9&W+N5y)b6^k+sB+9=3j7r3(sBDn!Zx{yT3mCphYNXUdSGRb0?VfsKYKrt6 z_`b?MnL#M}vRIIzg0!LYw3<4aPpMbxQ-5+Zlgi!F_HQZe;l!eMo}Yg~@t^T>0oPeC z=*tDTDg+!@&FEleG_7ZPOlG!=+kIP$PEyU-kw+$5i5=8#KM$`MAU$Bm1!3N>AHF zj|@@tl77_VY`WO5)|T##kK76=ChxA1IflvU@8>IDl84uq5nuajk!0VFpLr1{3HJ1^ zh(*SR5{-zaCi^kRXV;%6;H|ws`rv@3fN7)~Z_|yOfCvc$0-=F0M7(1XU`bT| zB0UKn_uN{CZaql_XEX+7Q=NI~sR|+FNia?S$;%C|hSIFxcrLt{!FdC0e)g%1fwpvb zJ(q4CtqDupMUY`2F2%I3*Eg(Mj}X+nvpqKz>4iK;Nhv4IkotN6AQc(X?{OncDkZRq zeA}9gUfmD~F+iI~&pDO6=c}?W5xaS!K2vyIK7+8W81$g-WVv}iGyk{`<#0gPG!IF7+LIC3>el?0r64`48FW-=DcbUBeBQu*-(x&(Zz|f-@Hu z^;JTiv}fIRc5|62dv+i^HCJq&UK|#E;1m(guhd!K)msXjDgSw-dw+jDp_amCSA~Ht!cSwnH zhP{^f(-SQHHk;ca8zml(!DEmAIYcZGYqU4#b_+G&rZ($4}|O z&ka2}wo1;Jn>6w}HIFt5H=MY+U>G22&|$IuwvDYI_8w~J;L4R6&ng?OQ^B#LlHaU_ z5uc&h3u8xV^)Vk-H{UUx>mc5pwit|YjVZgQMZG9O^G^m$rw*B*a%l~O7H z$hXc%ae1wBvSt$#BNkW}O8nxH+v3wcF&6f$U;zWGYqPT^cIpf|wm7fCLY`fnu6)?* zUU!-JEZ?_Ip19ue#xcyfvHF$clw#!I+T>8sJK|QeoeR-k^}3ODHA{;GZ(|wcIubIG7=;oGE@xCvFdr3o(7x0l fde~Dn?s*EpC3G^L5`7K;5=ncoGciiFMG6xCQ_?Pw6#^KQJZRMt)N!<*_0@? 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