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triangularize

triangularize([{10,9,...

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triangularize

triangularize([1,0,0]...

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triangularize

triangularize([3,1,1]...

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triangularize

triangularize([{10,9,...

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triangularize

triangularize([1,1,1,...

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triangularize

? triangularize;

Calculate

triangularize

? triangularize;

Calculate

triangularize

Run Example
(%i1)M: matrix ([1, 3, 6], [-3, -5, -6], [3, 3, 4]);
                               [  1    3    6  ]
                               [               ]
(%o1)                          [ - 3  - 5  - 6 ]
                               [               ]
                               [  3    3    4  ]
(%i2)  triangularize (M);
                                 [ 1  3  6  ]
                                 [          ]
(%o2)                            [ 0  4  12 ]
                                 [          ]
                                 [ 0  0  16 ]
(%i3) 
Run Example
p: c[1]*x+c[0];
(%o1)                              c  x + c
                                    1      0
(%i2) l1: [0,1,2,3];
(%o2)                            [0, 1, 2, 3]
(%i3) l2: [0,1,3,2];
(%o3)                            [0, 1, 3, 2]
(%i4) eqlist: makelist(subst([x=l1[ii]],p)-l2[ii],ii,1,4);
(%o4)           [c , c  + c  - 1, 2 c  + c  - 3, 3 c  + c  - 2]
                  0   1    0         1    0         1    0
(%i5) m: augcoefmatrix(eqlist,[c[0],c[1]]);
                                 [ 1  0   0  ]
                                 [           ]
                                 [ 1  1  - 1 ]
(%o5)                            [           ]
                                 [ 1  2  - 3 ]
                                 [           ]
                                 [ 1  3  - 2 ]
(%i6) m: triangularize(m);
                                 [ 1  0   0  ]
                                 [           ]
                                 [ 0  1  - 1 ]
(%o6)                            [           ]
                                 [ 0  0  - 1 ]
                                 [           ]
                                 [ 0  0   0  ]
(%i7) 
Run Example
m: matrix([1,2,3,4],[0,5,6,7],[0,1,1,1],[0,0,0,8],[0,0,0,9]);
                                [ 1  2  3  4 ]
                                [            ]
                                [ 0  5  6  7 ]
                                [            ]
(%o1)                           [ 0  1  1  1 ]
                                [            ]
                                [ 0  0  0  8 ]
                                [            ]
                                [ 0  0  0  9 ]
(%i2) rank(m);
(%o2)                                  4
(%i3) triangularize(m);
                              [ 1  2   3    4  ]
                              [                ]
                              [ 0  5   6    7  ]
                              [                ]
(%o3)                         [ 0  0  - 1  - 2 ]
                              [                ]
                              [ 0  0   0   - 8 ]
                              [                ]
                              [ 0  0   0    0  ]
(%i4) 
[addcol,display2d,false,flatten,matrix,ratsimp,solve,triangularize] [addcol,display2d,false,makelist,matrix,ratsimp,solve,triangularize] [addcol,display2d,load,makelist,matrix,ratsimp,solve,triangularize,true] [addcol,display2d,makelist,matrix,ratsimp,solve,triangularize,true] [addcol,ident,matrix,submatrix,triangularize] [addcol,length,makelist,matrix,transpose,triangularize] [addcol,length,makelist,matrix,triangularize] [addcol,matrix,triangularize,vandermonde_matrix] [augcoefmatrix,makelist,polymod,subst,triangularize] [coefmatrix,eliminate,length,makelist,rank,triangularize,unique] [coefmatrix,eliminate,length,makelist,rank,triangularize] [coefmatrix,length,makelist,rank,triangularize] [coefmatrix,length,makelist,triangularize] [col,matrix,rank,triangularize] [determinant,diagmatrix,eigenvalues,eigenvectors,invert,matrix,modulus,solve,transpose,triangularize] [determinant,diagmatrix,eigenvalues,eigenvectors,matrix,modulus,solve,transpose,triangularize] [determinant,diagmatrix,eigenvalues,eigenvectors,matrix,modulus,solve,triangularize] [determinant,diagmatrix,eigenvalues,matrix,modulus,solve,triangularize] [determinant,diagmatrix,eigenvectors,expand,factor,invert,matrix,modulus,solve,transpose,triangularize] [determinant,diagmatrix,eigenvectors,invert,matrix,modulus,solve,transpose,triangularize] [determinant,diagmatrix,matrix,modulus,solve,triangularize] [determinant,divide,expand,ident,matrix,mod,triangularize] [determinant,matrix,triangularize] [echelon,eliminate,matrix,triangularize] [echelon,ident,mat_fullunblocker,matrix,submatrix,transpose,triangularize] [echelon,matrix,transpose,triangularize] [echelon,matrix,triangularize] [eigenvalues,expand,matrix,minor,rat,solve,subst,transpose,triangularize] [eigenvalues,matrix,triangularize] [eigenvectors,matrix,triangularize] [ident,mat_fullunblocker,matrix,submatrix,triangularize] [linsolve,matrix,transpose,triangularize] [matrix,nullspace,triangularize] [matrix,rank,row,triangularize] [matrix,rank,transpose,triangularize] [matrix,rank,triangularize] [matrix,row,triangularize] [matrix,solve,transpose,triangularize] [matrix,solve,triangularize] [matrix,submatrix,transpose,triangularize] [matrix,transpose,triangularize] [matrix,triangularize,vandermonde_matrix] [matrix,triangularize] [triangularize]

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