Sponsored links: Algebra eBooks
 

Related

ident

I3:ident(3);

I3*4;

M:matrix[[1,0],[3,5]];

Calculate

ident-invert-matrix-ratsimp

A: matrix([1,t,-1],[t...

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

B: matrix([1],[1],[-1]);

Calculate

ident

I3:ident(3);

I3*4;

M:matrix[[1,0],[3,5]];

Calculate

ident-matrix

v1:[1156,624];

v2:[-203,-84];

m:matrix(v1,v2);

Calculate

ident-matrix-transpose

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

A:ident(3)-2/3*transp...

x1:A.transpose(matrix...

Calculate

ident

I2: ident(2);

M:matrix[[1,0],[3,5]];

M.I2;

Calculate

ident

I3:ident(3);

I3*4;

Calculate

ident-matrix-sqrt-transpose

e:matrix([1/sqrt(3),1...

A:ident(3)-2/3*transp...

A.transpose(matrix([1...

Calculate

ident

I2: ident(2);

M: matrix[ [1,0] . [3...

Calculate

ident-load-matrix-rank

load("diag");

C: matrix( [3,0,1,-2]...

Cp:C+ident(4);

Calculate

ident

Run Example
(%i1)e:matrix([sqrt(3)/3,sqrt(3)/3,sqrt(3)/3]);
                         [    1        1        1    ]
(%o1)                    [ -------  -------  ------- ]
                         [ sqrt(3)  sqrt(3)  sqrt(3) ]
(%i2) A:ident(3)-2/3*transpose(e).e;
                               [  7     2    2 ]
                               [  -   - -  - - ]
                               [  9     9    9 ]
                               [               ]
                               [   2   7     2 ]
(%o2)                          [ - -   -   - - ]
                               [   9   9     9 ]
                               [               ]
                               [   2    2   7  ]
                               [ - -  - -   -  ]
                               [   9    9   9  ]
(%i3) eigenvectors(A);
            1
(%o3)    [[[-, 1], [1, 2]], [[[1, 1, 1]], [[1, 0, - 1], [0, 1, - 1]]]]
            3
(%i4) A.transpose(A);
                             [  19     8     8  ]
                             [  --   - --  - -- ]
                             [  27     27    27 ]
                             [                  ]
                             [   8    19     8  ]
(%o4)                        [ - --   --   - -- ]
                             [   27   27     27 ]
                             [                  ]
                             [   8     8    19  ]
                             [ - --  - --   --  ]
                             [   27    27   27  ]
(%i5) 
Run Example
I2: ident(2);
                                   [ 1  0 ]
(%o1)                              [      ]
                                   [ 0  1 ]
(%i2) M: matrix[ [1,0] ,[3,5]];
(%o2)                        matrix
                                   [1, 0], [3, 5]
(%i3) M.I2;
                                   [ 1  0 ]
(%o3)                              [      ]
                                   [ 3  5 ]
(%i4) N: matrix [[1,3],[7,5]];
(%o4)                        matrix
                                   [1, 3], [7, 5]
(%i5) 
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,and,block,col,copy,fpprintprec,genmatrix,ident,invert,length,lmax,makelist,matrix_size,random,submatrix,sum,while] [addcol,echelon,ident,matrix,transpose] [addcol,echelon,ident,matrix] [apply,coeff,determinant,dim,expand,ident,makelist,sum] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,matrix,sqrt,transpose] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,sqrt,transpose] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,sqrt] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,subst,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,set_random_state,sqrt] [args,determinant,expand,factor,fullratsimp,ident,invert,matrix,solve,transpose] [args,determinant,expand,factor,ident,invert,matrix,solve,sqrt,transpose] [args,determinant,expand,factor,ident,invert,matrix,solve,transpose] [args,determinant,expand,factor,ident,matrix,solve,transpose] [asin,float,ident,mat_norm,matrix,max,sqrt,transpose] [asin,float,ident,mat_norm,matrix,sqrt,transpose] [batch,charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,determinant,eigenvalues,ident,invert,load,matrix] [coeff,determinant,expand,ident,matrix,sum] [determinant,divide,expand,ident,matrix,mod,solve] [determinant,divide,expand,ident,matrix,mod] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,eigenvectors,ident,load,matrix,ratsimp,solve,sqrt,transpose] [determinant,eigenvalues,ident,invert,matrix,rank,submatrix,transpose] [determinant,expand,factor,ident,matrix,solve] [determinant,expand,factor,ident,matrix] [determinant,expand,ident,matrix] [determinant,ident,invert,matrix,rank,submatrix,transpose] [determinant,ident,invert,matrix,submatrix,transpose] [determinant,ident,matrix] [echelon,ident,mat_fullunblocker,matrix,submatrix,transpose,triangularize] [eigenvectors,ident,matrix,nullity,nullspace] [eigenvectors,ident,matrix,sqrt,transpose] [eigenvectors,ident,matrix,transpose] [einstein,ident,load,sin,true] [factor,ident,invert,matrix] [genmatrix,ident,print,random] [ident,ilt,invert,matrix] [ident,invert,matrix,ratsimp] [ident,invert,matrix] [ident,load,matrix,rank] [ident,load,matrix] [ident,load] [ident,matrix,ratsimp] [ident,matrix,sqrt,transpose] [ident,matrix,transpose] [ident,matrix] [ident,transpose] [ident]

Related Help

Help for Ident