Sponsored links: Algebra eBooks
 

Related

invert-matrix-transpose

Z:matrix([1,0,1,0,0,0...

Z : transpose (Z);

invert (transpose(Z) ...

Calculate

invert-matrix

M:matrix([7,2,-2],[14...

A:invert(M);

Calculate

invert-kronecker_product-matrix-product

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

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

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

Calculate

invert-matrix

A:matrix([6,-9,5,4],[...

B:matrix([1,-1,-1,3],...

J:matrix([2,1,0,0],[0...

Calculate

invert-matrix-ratsimp-solve

a : matrix([1,c],[c,1]);

b : matrix([r1m], [r2...

x : matrix([r1],[r2]);

Calculate

invert-matrix

x:matrix([1,0,0],[0,c...

y:matrix([cy,0,sy],[0...

z:matrix([cz,-sz,0],[...

Calculate

invert-matrix

Q:matrix([0,0.2,0.1],...

D:matrix([500],[600],...

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

Calculate

invert-matrix

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

invert(a);

Calculate

invert-matrix-mod

m:matrix([9,18],[16,2...

n:matrix([1,18],[18,2...

mod((invert(m).n), 26);

Calculate

invert-matrix-transpose

A:matrix([7,0,-1,0,0]...

b:transpose(matrix([6...

x:invert(A).b;

Calculate

invert

Run Example
(%i1)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) 
Run Example
a: matrix([2, -1, 0], [0, 1, 1], [1, 1, 2]);
                                 [ 2  - 1  0 ]
                                 [           ]
(%o1)                            [ 0   1   1 ]
                                 [           ]
                                 [ 1   1   2 ]
(%i2) b: matrix([2, 3, -4], [4, 1, -1], [8, 4, -4]);
                                 [ 2  3  - 4 ]
                                 [           ]
(%o2)                            [ 4  1  - 1 ]
                                 [           ]
                                 [ 8  4  - 4 ]
(%i3) x: matrix([c, d, e], [f, g, h], [i, j, k]);
                                  [ c  d  e ]
                                  [         ]
(%o3)                             [ f  g  h ]
                                  [         ]
                                  [ i  j  k ]
(%i4) a . x = b;
           [   2 c - f      2 d - g      2 e - h   ]   [ 2  3  - 4 ]
           [                                       ]   [           ]
(%o4)      [    i + f        j + g        k + h    ] = [ 4  1  - 1 ]
           [                                       ]   [           ]
           [ 2 i + f + c  2 j + g + d  2 k + h + e ]   [ 8  4  - 4 ]
(%i5) solve(a . x = b, x);
(%o5)                                 []
(%i6) simplify(a .(invert(a) . b));
                                     [ 2  3  - 4 ]
                                     [           ]
(%o6)                       simplify([ 4  1  - 1 ])
                                     [           ]
                                     [ 8  4  - 4 ]
(%i7) 
[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] [addrow,invert,matrix,transpose] [adjoint,determinant,invert,matrix] [args,determinant,expand,factor,ident,invert,matrix,solve,transpose] [array,determinant,exp,invert,matrix,sin] [at,eigenvalues,invert,jacobian] [cos,invert,matrix,sin] [debugmode,invert,matrix,true] [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] [do,invert,matrix] [eigenvalues,eigenvectors,invert,matrix] [eigenvalues,invert,matrix] [eigenvectors,invert,matrix] [einstein,false,invert,kill,load,ratfac,ratriemann,rinvariant,scurvature,sin,true] [einstein,false,invert,kill,load,ratfac,ratriemann,rinvariant,scurvature,true] [expand,invert,matrix] [factor,ident,invert,matrix] [factor,invert,matrix] [float,invert,matrix] [fortran,invert,matrix] [hessian,invert,log,matrix] [invert,jacobian] [invert,kill,matrix,transpose] [invert,kronecker_product,matrix,product] [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,tex] [invert,matrix,transpose] [invert,matrix] [invert]

Related Help

Help for Invert