ࡱ> tvsj9 bjbj1GJl:::N***8R*l*lN6+++++///6888888$ ^\:/."///\jD++yjDjDjD/6l+:+6jD/6jDvjDFf ~X ,:6+*+ =hN*F? 60  ?:C0?6j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athcad, Mathematica, Derive, Mapple) ?>4A8AB5<, 2K?>;=ONI8E >?5@0F88 =04 <0B@8F0<8, 0 B0:65 ACI5AB2>20=85 A?5F80;L=KE ?@>3@0<<=KE 181;8>B5: (ScalaPack, PlaPack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aij (G8A5;, <0B5<0B8G5A:8E 2K@065=89), A>AB>OI0O 87 m AB@>: 8 n AB>;1F>2. A =  EMBED Equation.DSMT4  04 <0B@8F59 <>6=> ?@>872>48BL 459AB28O ?> ?@028;0< <0B@8G=>9 0;351@K. @8 m = n <0B@8F0 =07K205BAO :204@0B=>9, 0 G8A;> n  5Q ?>@O4:><. 01>@ M;5<5=B>2 <0B@8FK (a11, a22, & , ann) =07K205BAO 3;02=>9 4803>=0;LN. 5@E=5B@5C3>;L=>9 =07K205BAO <0B@8F0, 2 :>B>@>9 2A5 M;5<5=BK ?>4 3;02=>9 4803>=0;LN @02=K =C;N. A =  EMBED Equation.DSMT4  ?@545;5=85 <0B@8FK 2>7<>6=> B0:65 G5@57 ?>=OB85 5:B>@. 5:B>@  2 <0B5<0B8:5  =01>@ ai (G8A5;, <0B5<0B8G5A:8E 2K@065=89), A>AB>OI89 87 n M;5<5=B>2. ">340 0B@8F0 87 m AB@>: 8 n AB>;1F>2 <>65B 1KBL >?@545;5=0 :0: 5:B>@ 87 n M;5<5=B>2, 345 :064K9 M;5<5=B, 2 A2>N >G5@54L, O2;O5BAO 25:B>@>< 87 m M;5<5=B>2. ?5@0F88 =04 25:B>@0<8 CABL 7040=K 420 25:B>@0 A = (a1, a2, & , an) 8 B = (b1, b2, & , bn). 0AA<>B@8< A;54CNI85 >A=>2=K5 >?5@0F88 =04 25:B>@0<8: !@02=5=85 (A = B). 5:B>@0 AG8B0NBAO @02=K<8 B>340 8 B>;L:> B>340, :>340 ai = bi ?@8 2A5E i = 1..n. @8102;5=85 A:0;O@0 (A + a). 57C;LB0B>< A;>65=8O 25:B>@0 A 8 A:0;O@0 0 =07K205BAO 25:B>@ A = (a1 + a, a2 + a, & , an + a). KG8B0=85 A:0;O@0 (A + a). 57C;LB0B>< 2KG8B0=8O 25:B>@0 A 8 A:0;O@0 0 =07K205BAO 25:B>@ A = (a1 - a, a2 - a, & , an - a). #<=>65=85 =0 A:0;O@ (A * a). 57C;LB0B>< C<=>65=8O 25:B>@0 A =0 A:0;O@ 0 =07K205BAO 25:B>@ A = (a1 * a, a2 * a, & , an * a). KG8A;5=85 4;8=K. ;8=>9 25:B>@0 A =07K205BAO A:0;O@=0O 25;8G8=0 d = EMBED Equation.DSMT4 . !;>65=85 25:B>@>2 (A + B). 57C;LB0B>< A;>65=8O 25:B>@>2 A 8 B =07K205BAO 25:B>@ ! = (a1 + b1, a2 + b2, & , an + bn). KG8B0=85 25:B>@>2 (A  B). 57C;LB0B>< 2KG8B0=8O 25:B>@>2 A 8 B =07K205BAO 25:B>@ ! = (a1 - b1, a2 - b2, & , an - bn). !:0;O@=>5 ?@>872545=85 25:B>@>2 (A * B). !:0;O@=K< ?@>872545=85< 25:B>@>2 A 8 B =07K205BAO A:0;O@=0O 25;8G8=0 A =  EMBED Equation.DSMT4 . ?5@0F88 =04 <0B@8F0<8 CABL 7040=K 425 <0B@8FK A = (aij) 8 B = (bij) 8 25:B>@ V = (vj), 345 i = 1..m; j = 1..n. 0AA<>B@8< A;54CNI85 >A=>2=K5 >?5@0F88 =04 <0B@8F0<8: !@02=5=85 (A = B). 0B@8FK AG8B0NBAO @02=K<8 B>340 8 B>;L:> B>340, :>340 aij = bij ?@8 2A5E i = 1..m; j = 1..n. #<=>65=85 =0 A:0;O@ (A * d). 57C;LB0B>< C<=>65=8O <0B@8FK A =0 A:0;O@ d =07K205BAO <0B@8F0 D = (dij), 345 dij = aij * d, ?@8 2A5E i = 1..m; j = 1..n. #<=>65=85 =0 25:B>@ (A * V). 57C;LB0B>< C<=>65=8O <0B@8FK A =0 25:B>@ V =07K205BAO 25:B>@ D = (di), 345 di =  EMBED Equation.DSMT4 , ?@8 2A5E i = 1..m; j = 1..n. !;>65=85 <0B@8F (A + B). 57C;LB0B>< A;>65=8O <0B@8F A 8 B =07K205BAO <0B@8F0 C = (cij), 345 cij = aij + bij ?@8 2A5E i = 1..m; j = 1..n. KG8B0=85 <0B@8F (A  B). 57C;LB0B>< 2KG8B0=8O <0B@8F A 8 B =07K205BAO <0B@8F0 C = (cij), 345 cij = aij - bij ?@8 2A5E i = 1..m; j = 1..n. #<=>65=85 <0B@8F (A * B). 57C;LB0B>< C<=>65=8O <0B@8F A = (aij) 8 B = (bjk) =07K205BAO <0B@8F0 C = (cik), 345 cij = aij * bjk ?@8 2A5E i = 1..m; j = 1..n; k = 1..l. A=>2=K5 4>?CI5=8O !45;05< A;54CNI85 >A=>2=K5 4>?CI5=8O: #A;>28<AO @0AA<0B@820BL 2 40;L=59H5< 25@E=5B@5C3>;L=K5 :204@0B=K5 <0B@8FK, A>AB>OI85 87 M;5<5=B>2 ?@>872>;L=>3> B8?0. C45< AG8B0BL @07<5@ <0B@8FK :>=5G=K< G8A;><, =5 ?@52KH0NI8< 231. "@51>20=8O : ;01>@0B>@=>9 @01>B5  @0<:0E ;01>@0B>@=>9 @01>BK AB028BAO 7040G0 A>740=8O ?@>3@0<<=KE A@54AB2, ?>445@6820NI8E MDD5:B82=>5 E@0=5=85 <0B@8F A?5F80;L=>3> 2840 (25@E=5B@5C3>;L=KE) 8 2K?>;=5=85 >A=>2=KE >?5@0F89 =04 =8<8: A;>65=85/2KG8B0=85; C<=>65=85; :>?8@>20=85; A@02=5=85. @>3@0<<=K5 A@54AB20 4>;6=K 1KBL A>740=K ?@8 ?><>I8 2K1@0==>9 2 @0<:0E :C@A0  5B>4K ?@>3@0<<8@>20=8O A@54K ?@>3@0<<8@>20=8O 8 A>45@60BL: :;0AA 5:B>@ (=0 H01;>=0E); :;0AA 0B@8F0 (=0 H01;>=0E); A8AB5<C 287C0;870F88  8=B5@D59A=>5 ?@8;>65=85, ?>72>;ONI55 704020BL <0B@8FK 8 >ACI5AB2;OBL >A=>2=K5 >?5@0F88 =04 =8<8. #?@>I5==K9 20@80=B B@51>20=89 50;87>20BL :;0AA  <0B@8F0 , >15A?5G820NI89 E@0=5=85 <0B@8FK, 55 7040=85, 2K?>;=5=85 >?5@0F89 A;>65=8O 8 C<=>65=8O <0B@8F. >?CA:05BAO ?@54AB02;5=85 25@E=59 B@5C3>;L=>9 <0B@8FK 2 2845 42CE<5@=>3> <0AA820. 50;87>20BL :>=A>;L=>5 ?@8;>65=85, 45<>=AB@8@CNI55 @01>B>A?>A>1=>ABL @07@01>B0==>3> :;0AA0. @>5:B8@>20=85 40==KE 8 >?8A0=85 0;3>@8B<>2 !B@C:BC@K 40==KE 0: 8725AB=>, !B@C:BC@0 40==KE 5ABL <>45;L 40==KE 2 2845 0B5<0B8G5A:>9 AB@C:BC@K S = (M1, & , Mk, p1,& ,pn).  A>>B25BAB288 A MB8< <>6=> ?@825AB8 A;54CNI85 >?@545;5=8O: AB@C:BC@0 40==KE 5:B>@0 V = (v1, v2, & , vn) 5ABL Sv = (Mv pv), 345 Mv = {v1,v2, & , vn}  1078A=>5 <=>65AB2>,  EMBED Equation.DSMT4   >B=>H5=85 A;54>20=8O. !B@C:BC@0 40==KE 0B@8FK A = (aij), 345 i = 1..n; j = 1..n 5ABL Sa = (Ma, p1a, p2a), 345 Ma = {a11, a12, & , ann-1,ann}  1078A=>5 <=>65AB2>,  EMBED Equation.DSMT4   >B=>H5=8O A;54>20=8O. @8 >?@545;5=88 0B@8FK G5@57 5:B>@ (A = (vi), 345 vi  25:B>@ 87 n M;5<5=B>2) AB@C:BC@0 40==KE ?@8<5B 284: S1a = (M1a, p3a), 345 M1a = {v1, v2, & , vn}  1078A=>5 <=>65AB2>,  EMBED Equation.DSMT4   >B=>H5=8O A;54>20=8O. 0:>=5F, 4;O 25@E=5B@5C3>;L=>9 <0B@8FK 8<55B A<KA; 7040BL AB@C:BC@C 40==KE B0:8< >1@07><, GB>1K 8A:;NG8BL E@0=5=85 =C;52KE M;5<5=B>2. ?@545;5=85 <0B@8FK G5@57 25:B>@ ?>72>;O5B A45;0BL MB> =08;CGH8< >1@07><: S2a = (M2a, p4a), 345 M2a = {v1, v2, & , vn}  1078A=>5 <=>65AB2>, 345 vi 5ABL 25:B>@ 87 i M;5<5=B>2.  EMBED Equation.DSMT4   >B=>H5=8O A;54>20=8O.  EMBED PBrush  8A. 1 0B@8F0 :0: 25:B>@ 25:B>@=KE M;5<5=B>2 G5284=> AE>4AB2> 2 7040=88 AB@C:BC@K 40==KE 5:B>@, :0: =01>@0 M;5<5=B>2, A2O70==KE >B=>H5=85< A;54>20=8O, 8 AB@C:BC@K 40==KE 0B@8F0, :0: =01>@0 M;5<5=B>2-25:B>@>2, A2O70==KE >B=>H5=85< A;54>20=8O. -B>B D0:B ?>72>;O5B 548=>>1@07=> >@30=87>20BL 0;3>@8B<K >1@01>B:8 25:B>@>2 8 <0B@8F, 0, A;54>20B5;L=>, 8A?>;L7>20BL ?@8 @07@01>B:5 B@51C5<KE :;0AA>2 <5E0=87< =0A;54>20=8O. ;3>@8B<K 5:B>@ ;O AB@C:BC@K 40==KE 5:B>@ ?@54;0305BAO @50;87>20BL A;54CNI85 >?5@0F88: 2KG8A;5=85 4;8=K; A@02=5=85; ?@8102;5=85/2KG8B0=85 A:0;O@0; C<=>65=85 =0 A:0;O@; A;>65=85/2KG8B0=85 25:B>@>2; A:0;O@=>5 ?@>872545=85 25:B>@>2; A>740=85 :>?88. ;3>@8B<8G5A:8 2A5 >=8 >?8@0NBAO =0 D>@<C;K, ?@82545==K5 2 @0745;5 2. 5>1E>48<> >B<5B8BL, GB>, :@><5 >?5@0F89 2KG8A;5=8O 4;8=K 25:B>@0 8 A@02=5=8O 25:B>@>2, >AB0;L=K5 4>;6=K A>74020BL =>2K5 M:75<?;O@K AB@C:BC@K 40==KE 5:B>@. 0B@8F0 ;O AB@C:BC@K 40==KE 0B@8F0 ?@54;0305BAO @50;87>20BL A;54CNI85 >?5@0F88: A@02=5=85: A;>65=85/2KG8B0=85 <0B@8F: C<=>65=85 <0B@8F. 0: 8 2 A;CG05 A 25:B>@>< >?5@0F88 4;O AB@C:BC@K 40==KE 0B@8F0 >?8@0NBAO =0 D>@<C;K, ?@82545==K5 2 @0745;5 2. 07@01>B:0 ?@>3@0<<=>3> :><?;5:A0 >7<>6=0O <>4C;L=0O AB@C:BC@0 ?@>3@0<<K ! CG5B>< ?@54;>65==KE : @50;870F88 AB@C:BC@ 40==KE F5;5A>>1@07=>9 ?@54AB02;O5BAO A;54CNI0O <>4C;L=0O AB@C:BC@0 ?@>3@0<<K: Vector.h, Vector.cpp  <>4C;L, @50;87CNI89 AB@C:BC@C 40==KE 5:B>@; Matrix.h, Matrix.cpp  <>4C;L, @50;87CNI89 AB@C:BC@C 40==KE 0B@8F0; Main.h, Main.cpp, &  <>4C;L (<>4C;8) 3;02=>9 D>@<K 8=B5@D59A=>3> ?@8;>65=8O. !?5F8D8:0F88 <>4C;59 ! CG5B>< ?@54;>65==KE : @50;870F88 0;3>@8B<>2 >1@01>B:8 2K1@0==KE AB@C:BC@ 40==KE <>6=> A45;0BL A;54CNI85 >1JO2;5=8O :;0AA>2. ;0AA 5:B>@ (D09; Vector.h): template <class ValType> class TVector { protected: ValType *pVector; int Size; // @07<5@ 25:B>@0 int StartIndex; // 8=45:A ?5@2>3> M;5<5=B0 25:B>@0 public: TVector(int s = 10, int si = 0); // :>=AB@C:B>@ ?> C<>;G0=8N TVector(const TVector<ValType> &v); // :>=AB@C:B>@ :>?8@>20=8O ~TVector(); // int GetSize() { return Size; } // @07<5@ 25:B>@0 int GetStartIndex() { return StartIndex; } // 8=45:A ?5@2>3> M;5<5=B0 ValType & GetValue (int pos); // 4>ABC? A :>=B@>;5< 8=45:A0 ValType & operator[](int pos); // 4>ABC? int operator==(const TVector &v); // A@02=5=85 TVector & operator= (const TVector &v); // ?@8A20820=85 // A:0;O@=K5 >?5@0F88 TVector operator+ (const ValType &val); // ?@81028BL A:0;O@ TVector operator- (const ValType &val); // 2KG5ABL A:0;O@ TVector operator* (const ValType &val); // C<=>68BL =0 A:0;O@ // 25:B>@=K5 >?5@0F88 TVector operator+ (const TVector<ValType> &v); // A;>65=85 TVector operator- (const TVector<ValType> &v); // 2KG8B0=85 TVector operator* (const TVector<ValType> &v); // A:0;O@=>5 ?@>872545=85 // 22>4-2K2>4 friend istream & operator>>( istream &in, TVector<ValType> &v); friend ostream & operator<<( ostream &out, const TVector<ValType> &v); }; ;0AA 0B@8F0 (D09; Matrix.h): template <class ValType> class TMatrix : public TVector<TVector<ValType> > { public: TMatrix(int s = 10); // :>=AB@C:B>@ ?> C<>;G0=8N TMatrix(const TMatrix<ValType> &mt); // :>?8@>20=85 TMatrix(const TVector<TVector<ValType> > &mt); // ?@5>1@07>20=85 B8?0 TMatrix & operator==(const TMatrix<ValType> &mt); // A@02=5=85 TMatrix & operator= (const TMatrix<ValType> &mt); // ?@8A20820=85 TMatrix operator+ (const TMatrix<ValType> &mt); // A;>65=85 TMatrix operator- (const TMatrix<ValType> &mt); // 2KG8B0=85 TMatrix operator* (const TMatrix<ValType> &mt); // C<=>65=85 // 22>4 / 2K2>4 friend istream & operator>>(istream &in, TMatrix<ValType> &mt); friend ostream & operator<<(ostream &out, const TMatrix<ValType> &mt); }; -B0?K @07@01>B:8 @54;0305BAO A;54CNI0O ?>A;54>20B5;L=>ABL @07@01>B:8 8 @50;870F88 B@51C5<KE ?@>3@0<<=KE A@54AB2: >1JO2;5=85 :;0AA0 TVector; A>740=85 ?CAB>9 703>B>2:8 ?@>3@0<<K B5AB8@>20=8O; @50;870F8O :>=AB@C:B>@>2 8 45AB@C:B>@0; @50;870F8O <5B>4>2 22>40/2K2>40; >1JO2;5=85 25:B>@0 2 ?@>3@0<<5 B5AB8@>20=8O, 2K7>2 <5B>40 2K2>40 25:B>@0, 70?CA: B5AB8@CNI59 ?@>3@0<<K; >1JO2;5=85 :;0AA0 TMatrix; @50;870F8O :>=AB@C:B>@>2 8 45AB@C:B>@0; @50;870F8O <5B>4>2 22>40/2K2>40; >1JO2;5=85 <0B@8FK 2 ?@>3@0<<5 B5AB8@>20=8O, 2K7>2 <5B>40 2K2>40 <0B@8FK, 70?CA: B5AB8@CNI59 ?@>3@0<<K; @50;870F8O A:0;O@=KE >?5@0F89 2 :;0AA5 TVector, 8E ?@>25@:0 2 B5AB8@CNI59 ?@>3@0<<5; @50;870F8O >AB02H8EAO >?5@0F89 2 :;0AA5 TVector, 8E ?@>25@:0 2 B5AB8@CNI59 ?@>3@0<<5; @50;870F8O >?5@0F89 :;0AA0 TMatrix, 8E ?@>25@:0 2 B5AB8@CNI59 ?@>3@0<<5; A>740=85 8=B5@D59A=>3> ?@8;>65=8O (A<. @0745; 5). -;5<5=BK @50;870F88 ! CG5B>< A45;0==KE 2KH5 >1JO2;5=89 2K?8H5< 2>7<>6=CN @50;870F8N >?5@0F89 A>740=8O :>?88 (<5B>4 operator=) 4;O 25:B>@0 8 <0B@8FK. 5:B>@ template <class ValType> TVector<ValType> & TVector<ValType>::operator=(const TVector<ValType> &v) { if (this != &v) { if (Size != v.Size) { delete[] pVector; pVector = new ValType[v.Size]; } Size = v.Size; StartIndex = v.StartIndex; for (int i = 0; i < Size; i++) pVector[i] = v.pVector[i]; } return *this; } ><<5=B0@88: M;5<5=BK 25:B>@0 E@0=OBAO 2 48=0<8G5A:8 2K45;O5<>< =5?@5@K2=>< CG0AB:5 ?0<OB8 pVector; ?@8 =5A>2?045=88 @07<5@>2 8AE>4=>3> 8 :>?8@C5<>3> 25:B>@>2 =5>1E>48<> >A2>1>48BL 8 2K45;8BL 70=>2> ?0<OBL; >A=>2=0O G0ABL <5B>40  F8:;, ?>M;5<5=B=> :>?8@CNI89 7=0G5=8O. 0B@8F0 template <class ValType> TMatrix & TMatrix::operator=(const TMatrix &mt) { if (this != &mt) { if (Size != mt.Size) { delete[] pVector; pVector = new TVector[mt.Size]; } Size = mt.Size; StartIndex = mt.StartIndex; for (int i = 0; i < Size; i++) pVector[i] = mt.pVector[i]; } return *this; } ><<5=B0@88: <0B@8F0 E@0=8BAO :0: 25:B>@ 25:B>@>2 ?5@5<5==>9 4;8=K.  ?>;5 pVector :0640O OG59:0 E@0=8B C:070B5;L =0 >1J5:B :;0AA0 5:B>@; AB@>:0 pVector = new TVector<ValType>[mt.Size]; 2K45;O5B CG0AB>: ?0<OB8 4;O mt.Size >1J5:B>2 :;0AA0 5:B>@ (?@8 MB>< 4;O :064>3> 87 =8E ?@8 A>740=88 8A?>;L7C5BAO :>=AB@C:B>@ A ?0@0<5B@0<8 ?> C<>;G0=8N, CAB0=02;820NI89 @07<5@ 25:B>@0 @02=K9 10); AB@>:0 2 F8:;5 pVector[i] = mt.pVector[i]; 4;O :064>3> A>740==>3> >1J5:B0-25:B>@0 2K7K205B 53> >?5@0B>@ ?@8A20820=8O, :>B>@K9 CAB0=>28B ?@028;L=K9 @07<5@ 8 A:>?8@C5B M;5<5=BK. 5B@C4=> 70<5B8BL, GB> @50;870F8O <5B>4>2 ?@8A20820=8O 4;O 25:B>@0 8 <0B@8FK A>2?0405B A B>G=>ABLN 4> >1>7=0G5=89, 70 8A:;NG5=85< >4=>9 AB@>:8, 2K45;ONI59 ?0<OBL ?>4 =>2>5 :>;8G5AB2> M;5<5=B>2 ?>;O pVector. >A<>B@8< B5?5@L =0 @50;870F8N <5B>40 A;>65=8O 25:B>@>2. template <class ValType> TVector<ValType> TVector<ValType>::operator+(const TVector<ValType> &v) { TVector temp(Size, StartIndex); for (int i = 0; i < Size; i++) temp.pVector[i] = pVector[i] + v.pVector[i]; return temp; } K1@0==K9 =0<8 @0=55 A?>A>1 >?@545;5=8O <0B@8FK :0: 25:B>@0 25:B>@=KE M;5<5=B>2 ?>72>;O5B A45;0BL A;54CNI55 #B25@645=85 CABL <0B@8F0 A = (ai), 345 ai  25:B>@ 87 i M;5<5=B>2, <0B@8F0 B = (bi), 345 bi  25:B>@ 87 i M;5<5=B>2, B>340 @57C;LB0B>< A;>65=8O <0B@8F A 8 B 1C45B <0B@8F0 C = (ci), 345 ci  25:B>@ 87 i M;5<5=B>2 8 ci = ai + bi ?@8 2A5E i = 1..n; AB8==>ABL 40==>3> CB25@645=8O =5B@C4=> ?>:070BL. "0:65 >G5284=>, GB> ?>;CG5==K9 A?>A>1 2KG8A;5=8O AC<<K <0B@8F A>2?0405B A 40==K< 2 @0745;5 2 >?@545;5=85< AC<<K 25:B>@>2. "0:8< >1@07><, 4>;6=K A>2?040BL @50;870F88 <5B>4>2 A;>65=8O 4;O :;0AA0 5:B>@ 8 :;0AA0 0B@8F0, A B>9 ;8HL @07=8F59, GB> >?5@0F8O temp.pVector[i] = pVector[i] + v.pVector[i]; 2 A;CG05 A;>65=8O 25:B>@>2 AC<<8@C5B A:0;O@K, 0 2 A;CG05 A;>65=8O <0B@8F 4>;6=0 AC<<8@>20BL 25:B>@0. 0;8G85 >?5@0B>@0 A;>65=8O 25:B>@>2 8 B>B D0:B, GB> 2 :;0AA5 0B@8F0 :0640O OG59:0 ?>;O pVector E@0=8B C:070B5;L =0 >1J5:B :;0AA0 5:B>@, ?@82545B 8<5==> : B0:><C MDD5:BC.  @57C;LB0B5, @50;870F8O <5B>40 A;>65=8O <0B@8F <>65B 1KBL 70?8A0=0 A;54CNI8< >1@07><: template <class ValType> TMatrxi<ValType> & TMatrix<ValType>::operator+(const TMatrix<ValType> &mt) { return TVector<TVector<ValType>>::operator+(mt); } "5AB8@>20=85 ;O B5AB8@>20=8O A>740==KE :;0AA>2 <>6=> 8A?>;L7>20BL A;54CNICN ?@>3@0<<C (2 2K1@0==>9 A@545 ?@>3@0<<8@>20=8O =5>1E>48<> A>740BL :>=A>;L=>5 ?@8;>65=85). #include <iostream.h> #include <conio.h> #include <matrix.h> int main(int argc, char* argv[]) { TMatrix<int> a(5), b(5), c(5); int i, j; cout << ""5AB8@>20=85 ?@>3@0<< ?>445@6:8 ?@54AB02;5=8O B@5C3>;L=KE <0B@8F" << endl; for ( i=0; i<5; i++ ) for ( j=i; j<5; j++ ) { a[i][j] = i*10 + j; b[i][j] = (i*10 + j)*100; } c = a + b; cout << "Matrix a = " << endl << a << endl; cout << "Matrix b = " << endl << b << endl; cout << "Matrix c = a + b" << endl << c << endl; cout << "06<8B5 ;N1CN :;028HC" << endl; getch(); return 0; } 0;55 @5:><5=4C5BAO @07@01>B0BL 8=B5@D59A=>5 ?@8;>65=85, ?>72>;ONI55 ?@>25AB8 B5AB8@>20=85 2A5E @50;87>20==KE >?5@0F89. @54;>65=8O ?> >@30=870F88 ?>;L7>20B5;LA:>3> 8=B5@D59A0 0AA<>B@8< ?@>F5AA A>740=8O 8=B5@D59A=>3> ?@8;>65=8O. 5:><5=4C5BAO A;54CNI89 ?>@O4>: 459AB289. ;O :>=A>;L=>3> ?@8;>65=8O: !>740BL =>2>5 ?@8;>65=85. !>E@0=8BL 53>, ?@8A2>82 ?@>5:BC 8<O MatrixProject. >4:;NG8BL : ?@>5:BC D09;K Vector.cpp 8 Matrix.cpp. 50;87>20BL <5=N 2 A>AB025 ?C=:B>2  040=85 @07<5@0 <0B@8F ,  040=85 <0B@8FK 1 ,  040=85 <0B@8FK 2 ,  K?>;=5=85 A;>65=8O <0B@8F ,  K?>;=5=85 C<=>65=8O <0B@8F ,  K2>4 8AE>4=KE <0B@8F 8 @57C;LB0B0 ,  KE>4 . 50;87>20BL 459AB28O, C:070==K5 2 =0720=8OE ?C=:B>2 <5=N. ;O >:>==>3> ?@8;>65=8O: !>740BL =>2>5 ?@8;>65=85. !>E@0=8BL 53>, ?@8A2>82 ?@>5:BC 8<O MatrixProject, D09;C, A>45@60I5<C 3;02=CN D>@<C,  Main. 5@58<5=>20BL 3;02=CN D>@<C, ?@8A2>82 59 8<O frmMain 8 703>;>2>:  0B@8FK . ><5AB8BL =0 D>@<C ?0=5;L A <5B:>9  07<5@ <0B@8FK , AB@>:>9 22>40, :=>?:>9  !>740BL , :=>?:0<8  + ,  - ,  * . @8A2>8BL M;5<5=B0< C?@02;5=8O >A<KA;5==K5 8<5=0. K@>2=OBL ?0=5;L 225@E. ><5AB8BL =0 D>@<C 3 3@C??8@>2>G=KE M;5<5=B0  0B@8F0 A ,  0B@8F0 B ,  0B@8F0 - @57C;LB0B . 0 :064>< 87 =8E @07<5AB8BL B01;8FC. @8A2>8BL M;5<5=B0< C?@02;5=8O >A<KA;5==K5 8<5=0. >4:;NG8BL : ?@>5:BC D09;K Vector.cpp 8 Matrix.cpp. 50;87>20BL A>740=85 <0B@8F ?> =060B8N :=>?:8  !>740BL . 07<5@ AG8BK20BL 87 A>>B25BAB2CNI53> M;5<5=B0 C?@02;5=8O. 50;87>20BL 87<5=5=85 :>;8G5AB20 AB@>: 8 AB>;1F>2 B01;8F =0 D>@<5. 0?@5B8BL @540:B8@>20=85 B01;8FK  0B@8F0  @57C;LB0B . !8=E@>=878@>20BL 22>4 40==KE 2 B01;8FK  0B@8F0  8  0B@8F0 B A 70?>;=5=85< >1J5:B>2-<0B@8F 40==K<8. 50;87>20BL 2K?>;=5=85 459AB289 =04 <0B@8F0<8 ?> =060B8N :=>?>:  + ,  - ,  * . @30=87>20BL 2K2>4 @57C;LB8@CNI59 <0B@8FK 2 A>>B25BAB2CNICN B01;8FC. 50;87>20BL >1@01>B:C >H81>:, =0?@8<5@, >1@01>B:0 A;8H:>< 1>;LH>3> @07<5@0 <0B@8FK 8;8 =5G8A;>2KE 7=0G5=89.  >7<>6=K5 =0?@02;5=8O @0728B8O ?>AB0=>2:8 7040G8 ;O @0728B8O =02K:>2 ?@0:B8G5A:>3> ?@>3@0<<8@>20=8O @5:><5=4CNBAO A;54CNI85 =0?@02;5=8O @0AH8@5=8O ?>AB0=>2:8 7040G8: 50;870F8O 4@C38E A?>A>1>2 ?@54AB02;5=8O <0B@8F A?5F80;L=>3> 2840 4;O ?@>2545=8O 2KG8A;8B5;L=KE M:A?5@8<5=B>2 A F5;LN A@02=5=8O MDD5:B82=>AB8 E@0=5=8O 8 >1@01>B:8 <0B@8F (E@0=5=85 157 8A:;NG5=8O =C;52KE M;5<5=B>2, ?;>B=>5 8A?>;L7>20=85 ?0<OB8  8A:;NG5=85 M;5<5=B>2 =865 3;02=>9 4803>=0;8). 50;870F8O 4>?>;=8B5;L=KE >?5@0F89 =04 <0B@8F0<8  B@0=A?>=8@>20=85, 2KG8A;5=85 >?@545;8B5;O, @0=30, >1@0B=>9 <0B@8FK, ?@>25@:0 =0 ?>4>185. 5H5=85 7040G8 ?@82545=8O <0B@8FK : B@5C3>;L=><C 284C. 5H5=85 A8AB5< ;8=59=KE C@02=5=89. 07@01>B:0 MDD5:B82=KE 0;3>@8B<>2 <0B@8G=>3> C<=>65=8O A 8A?>;L7>20=85< 2>7<>6=>AB59 8 ?@8=F8?>2 @01>BK A>2@5<5==KE ?@>F5AA>@>2. !@02=5=85 @07=KE @50;870F89 (?@>2545=85 2KG8A;8B5;L=KE M:A?5@8<5=B>2 ?@8 1>;LH8E ?>@O4:0E <0B@8F).  ," #8;LO< >C0= (1805-1865) - 8@;0=4A:89 <0B5<0B8:, 8=>AB@0==K9 G;5=-:>@@5A?>=45=B 5B5@1C@3A:>9  (1837). 0; B>G=>5 D>@<0;L=>5 87;>65=85 B5>@88 :><?;5:A=KE G8A5;. >AB@>8; A8AB5<C G8A5; - :20B5@=8>=>2.  <5E0=8:5 40; >1I89 ?@8=F8? =08<5=LH53> 459AB28O.  - @BC@ (1821-1895) - 0=3;89A:89 <0B5<0B8:, 8=>AB@0==K9 G;5=-:>@@5A?>45=B 5B5@1C@3A:>9  (1870). 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