### Related

##### 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

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)

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