# LaTeX2HTML 0.6.4 (Tues Aug 30 1994)
# Associate image original text (scrambled) with physical files.

$key = q/{}$leftarrowvec_N(X)^Tvec_N(Y)${}/;
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$key = q/{tabular}cccttTRANS=`N';html_special_mark_amp;;html_special_mark_amp;$vec_N(Y)leftarrowsub_N,N(A)^-1sub_N(X)$ttTRANS=`T';html_special_mark_amp;;html_special_mark_amp;$vec_N(Y)leftarrowsub_N,N(A)^-Tsub_N(X)$ttTRANS=`C';html_special_mark_amp;;html_special_mark_amp;$vec_N(Y)leftarrowsub_N,N(A)^-Hsub_N(X)${tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular569.gif">'; 
$key = q/{}$T${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1578.gif">'; 
$key = q/{tabular}llttP$Box$SYMM(;html_special_mark_amp;ttSIDE,UPLO,M,N,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB,BETA,C,IC,JC,DESCC)ttP$Box$HEMM(;html_special_mark_amp;ttSIDE,UPLO,M,N,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB,BETA,C,IC,JC,DESCC){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular677.gif">'; 
$key = q/{}$(-10.0^10)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2084.gif">'; 
$key = q/{}$N${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2136.gif">'; 
$key = q/{}$10.0^10${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2086.gif">'; 
$key = q/{}$epsilon^-1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2088.gif">'; 
$key = q/{}$leftarrow~beta${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1690.gif">'; 
$key = q/{}$beta${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1740.gif">'; 
$key = q/{}$ttC(1:4,1:4)leftarrowA(1:4,1:4)*B(1:4,1:4)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2118.gif">'; 
$key = q/{}$sub_N,N(C)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1960.gif">'; 
$key = q/{}$xleftarrowTx${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1518.gif">'; 
$key = q/{}$DESC_(1)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2110.gif">'; 
$key = q/{tabular}llttP$Box$GER$Box$(;html_special_mark_amp;ttM,N,ALPHA,X,IX,JX,DESCX,INCX,Y,IY,JY,DESCY,INCY,;html_special_mark_amp;ttA,IA,JA,DESCA){tabular}/;
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$key = q/{tabular}llttP$Box$SYR2K(;html_special_mark_amp;ttUPLO,TRANS,N,K,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB,BETA,C,IC,JC,DESCC)ttP$Box$HER2K(;html_special_mark_amp;ttUPLO,TRANS,N,K,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB,BETA,C,IC,JC,DESCC){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular753.gif">'; 
$key = q/{}$vec_N(X)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1758.gif">'; 
$key = q/{}$B${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1574.gif">'; 
$key = q/{}$A,B${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2122.gif">'; 
$key = q/{}$k=1~to~Nr${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2146.gif">'; 
$key = q/{}$~;html_special_mark_lt;0${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1724.gif">'; 
$key = q/{tabular}llll;html_special_mark_amp;bfS;html_special_mark_amp;;html_special_mark_amp;REAL;html_special_mark_amp;bfD;html_special_mark_amp;;html_special_mark_amp;DOUBLEPRECISION;html_special_mark_amp;bfC;html_special_mark_amp;;html_special_mark_amp;COMPLEX;html_special_mark_amp;bfZ;html_special_mark_amp;;html_special_mark_amp;COMPLEX*16orDOUBLECOMPLEX(ifavailable){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular142.gif">'; 
$key = q/{}$dotleftarrowx^Ty${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1496.gif">'; 
$key = q/{}$y${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1570.gif">'; 
$key = q/{}$-1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2112.gif">'; 
$key = q/{}$sub(C)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1884.gif">'; 
$key = q/{tabular}llttP$Box$GEMV(;html_special_mark_amp;ttTRANS,M,N,ALPHA,A,IA,JA,DESCA,X,IX,JX,DESCX,INCX,;html_special_mark_amp;ttBETA,Y,IY,JY,DESCY,INCY){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular514.gif">'; 
$key = q/{tabular}clr;html_special_mark_amp;Factorpanel$B$withpivoting,;html_special_mark_amp;(ttP$Box$AMAX,P$Box$SWAP,P$Box$GER$Box$);html_special_mark_amp;Applypivotstotheremainderofthematrix,;html_special_mark_amp;(ttP$Box$SWAP);html_special_mark_amp;Solve$C:=B1^-1C$,;html_special_mark_amp;(Triangularsolve,ttP$Box$TRSM);html_special_mark_amp;Update$E:=E-B2*C$,;html_special_mark_amp;(Rank-$r$update,ttP$Box$GEMM){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular992.gif">'; 
$key = q/{}$(0,0)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2130.gif">'; 
$key = q/{}$sub_M,N(B)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2032.gif">'; 
$key = q/{}$~;html_special_mark_lt;~0${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1702.gif">'; 
$key = q/{}$2k${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1536.gif">'; 
$key = q/{}$2${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1864.gif">'; 
$key = q/{}$leftarrow|re(vec_N(X))|_1+|im(vec_N(X))|_1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1790.gif">'; 
$key = q/{}$sub_K,N(B)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1896.gif">'; 
$key = q/{}$sub_N,N(A)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1872.gif">'; 
$key = q/{}$~;html_special_mark_gt;~${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1712.gif">'; 
$key = q/{}$k${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1952.gif">'; 
$key = q/{tabular}llttP$Box$SYR2(;html_special_mark_amp;ttUPLO,N,ALPHA,X,IX,JX,DESCX,INCX,Y,IY,JY,DESCY,INCY,;html_special_mark_amp;ttA,IA,JA,DESCA)ttP$Box$HER2(;html_special_mark_amp;ttUPLO,N,ALPHA,X,IX,JX,DESCX,INCX,Y,IY,JY,DESCY,INCY,;html_special_mark_amp;ttA,IA,JA,DESCA){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular621.gif">'; 
$key = q/{}$~neq~1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1730.gif">'; 
$key = q/{}$-DESC_(1)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2114.gif">'; 
$key = q/{}$sub(B)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2056.gif">'; 
$key = q/{tabular}llttP$Box$TRSM(;html_special_mark_amp;ttSIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular857.gif">'; 
$key = q/{}$sub_N,K(B)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1898.gif">'; 
$key = q/{figure}[h]centerlinepsfigfigure=lufact.ps,height=2.8in,width=2.8in{figure}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_figure985.gif">'; 
$key = q/{figure}[h]centerlinepsfigfigure=mat5.ps,height=2.2in,width=5.2in{figure}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_figure235.gif">'; 
$key = q/{}$xleftrightarrowy${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1480.gif">'; 
$key = q/{}$^S${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1476.gif">'; 
$key = q/{}$asumleftarrow|re(x)|_1+|im(x)|_1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1504.gif">'; 
$key = q/{}$~geq~Q${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1726.gif">'; 
$key = q/{table}centeringtabularcccccccccchlineReal;html_special_mark_amp;Complex;html_special_mark_amp;ttMM;html_special_mark_amp;ttMV;html_special_mark_amp;ttR;html_special_mark_amp;ttR2;html_special_mark_amp;ttRK;html_special_mark_amp;ttR2K;html_special_mark_amp;ttSM;html_special_mark_amp;ttSVhlinettPSGE;html_special_mark_amp;ttPCGE;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;ttPSSY;html_special_mark_amp;ttPCSY;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;ttPCHE;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;;html_special_mark_amp;ttPSTR;html_special_mark_amp;ttPCTR;html_special_mark_amp;*;html_special_mark_amp;*;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;;html_special_mark_amp;*;html_special_mark_amp;*hlinemulticolumn10lMatrixtransposition:ttPSTRAN,ttPCTRANUandttPCTRANC.hlinetabularlabeltab:level23{table}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_table204.gif">'; 
$key = q/{}$~times~${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2120.gif">'; 
$key = q/{}$downarrow${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2170.gif">'; 
$key = q/{}$P~times~Q${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1658.gif">'; 
$key = q/{}$sub(A)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2060.gif">'; 
$key = q/{}$K${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1686.gif">'; 
$key = q/{}$sub_M,K(A)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1890.gif">'; 
$key = q/{}$sub_M,N(C)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1886.gif">'; 
$key = q/{}$(-1.0,1.0)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2082.gif">'; 
$key = q/{}$xleftarrowT^-1x${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1522.gif">'; 
$key = q/{tabular}llttP$Box$SYMV(;html_special_mark_amp;ttUPLO,N,ALPHA,A,IA,JA,DESCA,X,IX,JX,DESCX,INCX,;html_special_mark_amp;ttBETA,Y,IY,JY,DESCY,INCY)ttP$Box$HEMV(;html_special_mark_amp;ttUPLO,N,ALPHA,A,IA,JA,DESCA,X,IX,JX,DESCX,INCX,;html_special_mark_amp;ttBETA,Y,IY,JY,DESCY,INCY){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular533.gif">'; 
$key = q/{}$C${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2134.gif">'; 
$key = q/{}$xleftarrowT^-Tx${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1524.gif">'; 
$key = q/{}$yleftarrowx${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1488.gif">'; 
$key = q/{}$A${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1572.gif">'; 
$key = q/{}$leftarrowvec_N(X)^Hvec_N(Y)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1782.gif">'; 
$key = q/{}$epsilon^-1over2${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2090.gif">'; 
$key = q/{}$vec_N(X)leftrightarrowvec_N(Y)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1762.gif">'; 
$key = q/{tabular}llttP$Box$TRMM(;html_special_mark_amp;ttSIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular832.gif">'; 
$key = q/{displaymath}left{arrayllttINDXleftarrow;html_special_mark_amp;1^st~kni|re(vec_N(X)_k)|+|im(vec_N(X)_k)|;html_special_mark_amp;=max(|re(vec_N(X)_i)|+|im(vec_N(X)_i)|)ttAMAXleftarrow;html_special_mark_amp;vec_N(X)_karrayright.{displaymath}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_displaymath1755.gif">'; 
$key = q/{}$2times2${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1662.gif">'; 
$key = q/{}$~;html_special_mark_lt;~1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1718.gif">'; 
$key = q/{}$x${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1568.gif">'; 
$key = q/{}$xleftarrowT^Tx${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1520.gif">'; 
$key = q/{tabular}llValue;html_special_mark_amp;Meaninghlinett`U';html_special_mark_amp;Unittriangular.tt`R';html_special_mark_amp;Non-unittriangular.{tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular314.gif">'; 
$key = q/{}$vec_N(Y)leftarrowvec_N(X)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1770.gif">'; 
$key = q/{}$100*i+j${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1736.gif">'; 
$key = q/{}$sub_M,M(A)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1940.gif">'; 
$key = q/{}$r${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2144.gif">'; 
$key = q/{}$1${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap2106.gif">'; 
$key = q/{}$times~${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1692.gif">'; 
$key = q/{tabular}llValue;html_special_mark_amp;Meaninghlinett`U';html_special_mark_amp;Uppertriangle.tt`L';html_special_mark_amp;Lowertriangle.{tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular306.gif">'; 
$key = q/{}$leftarrow|vec_N(X)|_2${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1786.gif">'; 
$key = q/{}$ast${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1604.gif">'; 
$key = q/{tabular}llValue;html_special_mark_amp;Meaninghlinett`N';html_special_mark_amp;Operatewiththedistributedmatrix.tt`T';html_special_mark_amp;Operatewiththetransposeofthedistributedmatrix.tt`C';html_special_mark_amp;Operatewiththeconjugatetransposeofthedistributedmatrix.{tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular294.gif">'; 
$key = q/{}$~;html_special_mark_lt;~${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1728.gif">'; 
$key = q/{}$nrm2leftarrow|x|_2${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1500.gif">'; 
$key = q/{tabular}cccttTRANS=`N';html_special_mark_amp;;html_special_mark_amp;$vec_N(X)leftarrowsub_N,N(A)vec_N(X)$ttTRANS=`T';html_special_mark_amp;;html_special_mark_amp;$vec_N(X)leftarrowsub_N,N(A)^Tvec_N(X)$ttTRANS=`C';html_special_mark_amp;;html_special_mark_amp;$vec_N(X)leftarrowsub_N,N(A)^Hvec_N(X)${tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular554.gif">'; 
$key = q/{}$sub_K,M(A)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1892.gif">'; 
$key = q/{tabular}llttP$Box$GEMM(;html_special_mark_amp;ttTRANSA,TRANSB,M,N,K,ALPHA,A,IA,JA,DESCA,;html_special_mark_amp;ttB,IB,JB,DESCB,BETA,C,IC,JC,DESCC){tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular649.gif">'; 
$key = q/{}$sub_M,N(A)${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1794.gif">'; 
$key = q/{displaymath}vec_N(X)=left{arraylttX(IX,JX:JX+N-1)rm~if~ttINCX=DESCX(1)rm~and~ttX(IX:IX+N-1,JX)rm~if~ttINCX=1.arrayright.{displaymath}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_displaymath1754.gif">'; 
$key = q/{tabular}llll;html_special_mark_amp;bfGE;html_special_mark_amp;;html_special_mark_amp;AllmatrixoperandsareGEneralrectangular;;html_special_mark_amp;bfHE;html_special_mark_amp;;html_special_mark_amp;OneofthematrixoperandsisHErmitian;;html_special_mark_amp;bfSY;html_special_mark_amp;;html_special_mark_amp;OneofthematrixoperandsisSYmmetric;;html_special_mark_amp;bfTR;html_special_mark_amp;;html_special_mark_amp;OneofthematrixoperandsisTRiangular.{tabular}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tabular151.gif">'; 
$key = q/{}$~geq~P${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1722.gif">'; 
$key = q/{}$5times5${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1468.gif">'; 
$key = q/{}$Box${}/;
$cached_env_img{$key} ='<IMG ALIGN=BOTTOM SRC="_13985_tex2html_wrap1876.gif">'; 
$key = q/{}$~neq~${}/;
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$key = q/{tabular}llValue;html_special_mark_amp;Meaninghlinett`L';html_special_mark_amp;Multiplygeneraldistributedmatrixbysymmetricortriangular;html_special_mark_amp;distributedmatrixontheleft.tt`R';html_special_mark_amp;Multiplygeneraldistributedmatrixbysymmetricortriangular;html_special_mark_amp;distributedmatrixontheright.{tabular}/;
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1;