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invert-matrix

A: matrix([1,r12,r13]...

invert(A);

Calculate

invert-matrix

t:matrix([0, 0, 0,1],...

p: matrix([a, 1-b, 0,...

invert(t).p.t;

Calculate

invert-matrix-transpose

a: matrix ([1, 1, 1],...

transpose(a).invert(a...

Calculate

invert-matrix-phi-transpose

a:matrix([-4,2,-2],[2...

q:matrix([1,0,1],[0,1...

p9:matrix([9,0,0],[0,...

Calculate

invert-matrix-ratsimp

M: matrix([m1/k1, 0],...

K: matrix([(k1+k2)/k1...

b: matrix([1], [0]);

Calculate

invert-matrix-ratsimp

ip_n: matrix([i11,i12...

tx_n: matrix([t11,t12...

op_n: matrix([o11,o12...

Calculate

invert-matrix

x: matrix([1,2],[3,4]);

inv_x: invert(x);

x.inv_x;

Calculate

invert-load-matrix-row

load(eigen);

v3: columnvector([pa3...

v4:columnvector([pa4,...

Calculate

invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([gh*Ih, ...

C: invert (B);

Calculate

invert-matrix-transpose

a:matrix([0,0,1,0,0],...

invert(a);

transpose(a);

Calculate

invert

Run Example
(%i1)alpha1: %pi/2;
                                      %pi
(%o1)                                 ---
                                       2
(%i2) alpha2: -%pi/2;
                                       %pi
(%o2)                                - ---
                                        2
(%i3) beta1: 0;
(%o3)                                  0
(%i4) beta2: %pi;
(%o4)                                 %pi
(%i5) l1:0.20;
(%o5)                                 0.2
(%i6) l2: l1;
(%o6)                                 0.2
(%i7) r1: .05;
(%o7)                                0.05
(%i8) r2: .05;
(%o8)                                0.05
(%i9) teta: 0;
(%o9)                                  0
(%i10) W: invert(matrix( [r1, 0], [0, r2] ));
                                [ 20.0   0   ]
(%o10)                          [            ]
                                [  0    20.0 ]
(%i11) CP: matrix( [sin(alpha1 + beta1), -cos(alpha1 + beta1), -l1*cos(beta1)], [sin(alpha2 + beta2), -cos(alpha2 + beta2), -l2*cos(beta2)] );
                                [ 1  0  - 0.2 ]
(%o11)                          [             ]
                                [ 1  0   0.2  ]
(%i12) R: matrix( [cos(teta), sin(teta), 0], [-sin(teta), cos(teta), 0], [0, 0, 1] );
                                  [ 1  0  0 ]
                                  [         ]
(%o12)                            [ 0  1  0 ]
                                  [         ]
                                  [ 0  0  1 ]
(%i13) E = matrix([0, 0, %pi/4]);
                                   [       %pi ]
(%o13)                         E = [ 0  0  --- ]
                                   [        4  ]
(%i14) phi = W.CP.R.E;
                                                    [ 1  0  0 ]
                 [ 20.0   0   ]   [ 1  0  - 0.2 ]   [         ]
(%o14)     phi = [            ] . [             ] . [ 0  1  0 ] . E
                 [  0    20.0 ]   [ 1  0   0.2  ]   [         ]
                                                    [ 0  0  1 ]
(%i15) 
Run Example
v1:[1,0,1];
(%o1)                              [1, 0, 1]
(%i2) v2:[0,1,0];
(%o2)                              [0, 1, 0]
(%i3) v3:[0,1,1];
(%o3)                              [0, 1, 1]
(%i4) v4:[1,2,3];
(%o4)                              [1, 2, 3]
(%i5) v5:[1,3,0];
(%o5)                              [1, 3, 0]
(%i6) v6:[3,2,3];
(%o6)                              [3, 2, 3]
(%i7) B1:matrix(v1,v2,v3);
                                  [ 1  0  1 ]
                                  [         ]
(%o7)                             [ 0  1  0 ]
                                  [         ]
                                  [ 0  1  1 ]
(%i8) B2:matrix(v4,v5,v6);
                                  [ 1  2  3 ]
                                  [         ]
(%o8)                             [ 1  3  0 ]
                                  [         ]
                                  [ 3  2  3 ]
(%i9) rank(B1);
(%o9)                                  3
(%i10) rank(B2);
(%o10)                                 3
(%i11) A:B2.(invert(B1));
                                 [ 1  0   2  ]
                                 [           ]
(%o11)                           [ 1  4  - 1 ]
                                 [           ]
                                 [ 3  2   0  ]
(%i12) 
Run Example
m:matrix([1,2,3],[4,7,9]);
                                  [ 1  2  3 ]
(%o1)                             [         ]
                                  [ 4  7  9 ]
(%i2) m2:submatrix(m,3);
                                   [ 1  2 ]
(%o2)                              [      ]
                                   [ 4  7 ]
(%i3) m3:submatrix(1,m);
(%o3)                             [ 4  7  9 ]
(%i4) transpose(m);
                                   [ 1  4 ]
                                   [      ]
(%o4)                              [ 2  7 ]
                                   [      ]
                                   [ 3  9 ]
(%i5) invert(m2);
                                 [ - 7   2  ]
(%o5)                            [          ]
                                 [  4   - 1 ]
(%i6) determinant(m2);
(%o6)                                 - 1
(%i7) m2.invert(m2);
                                   [ 1  0 ]
(%o7)                              [      ]
                                   [ 0  1 ]
(%i8) ident(2);
                                   [ 1  0 ]
(%o8)                              [      ]
                                   [ 0  1 ]
(%i9) rank(m);
(%o9)                                  2
(%i10) eigenvalues(m2);
(%o10)              [[4 - sqrt(17), sqrt(17) + 4], [1, 1]]
(%i11) eigenvectors(m2);
(%o11) [[[4 - sqrt(17), sqrt(17) + 4], [1, 1]], 
                                          sqrt(17) - 3         sqrt(17) + 3
                                  [[[1, - ------------]], [[1, ------------]]]]
                                               2                    2
(%i12) m2.invert(m2)-ident(2);
                                   [ 0  0 ]
(%o12)                             [      ]
                                   [ 0  0 ]
(%i13) 
[abs,carg,float,invert,matrix,polarform,ratsimp,rectform] [addcol,addrow,diff,do,ev,genmatrix,invert,kill,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [adjoint,determinant,invert,matrix] [args,determinant,expand,factor,ident,invert,matrix,solve,transpose] [array,determinant,exp,invert,matrix,sin] [at,eigenvalues,invert,jacobian] [cabs,carg,invert,matrix,plot2d] [cos,determinant,invert,mat_trace,matrix,numer,sin,trace,transpose,true] [cos,eigenvalues,invert,matrix,numer,sin,transpose,true] [cos,invert,matrix,numer,sin,transpose,true] [cos,invert,matrix,sin] [determinant,diagmatrix,eigenvectors,invert,matrix,modulus,solve,transpose,triangularize] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,float,invert,matrix,transpose] [determinant,ident,invert,matrix,submatrix,transpose] [determinant,invert,matrix,permanent] [determinant,invert,matrix,solve] [determinant,invert,matrix,submatrix,transpose] [determinant,invert,matrix,transpose] [determinant,invert,matrix] [determinant,invert,transpose] [determinant,invert] [detout,doallmxops,doscmxops,exp,false,invert,matrix,sqrt,true] [detout,factor,invert,matrix] [eigenvalues,eigenvectors,invert,matrix] [eigenvalues,invert,matrix] [eigenvectors,invert,matrix] [einstein,false,invert,kill,load,ratfac,ratriemann,rinvariant,scurvature,sin,true] [expand,invert,matrix] [factor,ident,invert,matrix] [factor,invert,matrix] [false,invert,load,rateinstein,ratfac,ratriemann,sin,true] [float,invert,matrix,transpose] [float,invert,matrix] [fullratsimp,invert,matrix] [invert,jacobian] [invert,kill,matrix,transpose] [invert,load,matrix] [invert,matrix,mod] [invert,matrix,numer] [invert,matrix,phi,transpose] [invert,matrix,rank,transpose] [invert,matrix,rank] [invert,matrix,ratsimp] [invert,matrix,solve] [invert,matrix,sqrt] [invert,matrix,transpose] [invert,matrix] [invert]

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