### Related

##### true

t1: a1;

t2: a0;

t3: a2;

Calculate

obj : 0.043*x1+0.027*...

cnst : [x1+x2+x3+x4+x...

Calculate

##### matrix

mry:matrix([ct,0,st,0...

mrz:matrix([cp,-sp,0,...

mt:matrix([1,0,0,tx],...

Calculate

tosi: true;

tosi;

Calculate

##### length

length(primes(1,150));

Calculate

s:[1,2,3,4,5,6,7,8,9,...

Calculate

A:create_graph([0,1,2...

draw_graph(A,show_id=...

Calculate

##### matrix-sqrt

m: matrix([5/4*k-w*w*...

%, w*w=3;

Calculate

##### matrix-matrixp

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

matrixp(m);

Calculate

A : 1;

B : 2;

Calculate

Run Example
```(%i1)load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) P: matrix([0,1,0],[0,0,1],[1,0,0]);
[ 0  1  0 ]
[         ]
(%o2)                             [ 0  0  1 ]
[         ]
[ 1  0  0 ]
(%i3) Pdag: ctranspose(P);
[ 0  0  1 ]
[         ]
(%o3)                             [ 1  0  0 ]
[         ]
[ 0  1  0 ]
(%i4) A: P+Pdag;
[ 0  1  1 ]
[         ]
(%o4)                             [ 1  0  1 ]
[         ]
[ 1  1  0 ]
(%i5) hermitianmatrix: true;
(%o5)                                true
(%i6) [vals, vecs] = uniteigenvectors(A);
(%o6) [vals, vecs] = [[[2, - 1], [1, 2]],
1        1        1            1             1
[[[-------, -------, -------]], [[-------, 0, - -------],
sqrt(3)  sqrt(3)  sqrt(3)      sqrt(2)       sqrt(2)
1         sqrt(2)           1
[- ---------------, -------, - ---------------]]]]
sqrt(2) sqrt(3)  sqrt(3)    sqrt(2) sqrt(3)
(%i7) vals[1];
(%o7)                                vals
1
(%i8) length (vals[1]);
(%o8)                                  1
(%i9) for i:1 thru length(vals[1]) do disp (val[i] = vals[1][i],  mult[i] = vals[2][i], vec[i] = vecs[i]);
val  = (vals )
1        1
1

mult  = (vals )
1        2
1

vec  = vecs
1       1

(%o9)                                done
(%i10) P2: matrix([0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0]);
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
(%o10)                 [                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
(%i11) ```
Run Example
```load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) P: matrix([0,1,0],[0,0,1],[1,0,0]);
[ 0  1  0 ]
[         ]
(%o2)                             [ 0  0  1 ]
[         ]
[ 1  0  0 ]
(%i3) Pdag: ctranspose(P);
[ 0  0  1 ]
[         ]
(%o3)                             [ 1  0  0 ]
[         ]
[ 0  1  0 ]
(%i4) A: P+Pdag;
[ 0  1  1 ]
[         ]
(%o4)                             [ 1  0  1 ]
[         ]
[ 1  1  0 ]
(%i5) hermitianmatrix: true;
(%o5)                                true
(%i6) [vals, vecs] = uniteigenvectors(A);
(%o6) [vals, vecs] = [[[2, - 1], [1, 2]],
1        1        1            1             1
[[[-------, -------, -------]], [[-------, 0, - -------],
sqrt(3)  sqrt(3)  sqrt(3)      sqrt(2)       sqrt(2)
1         sqrt(2)           1
[- ---------------, -------, - ---------------]]]]
sqrt(2) sqrt(3)  sqrt(3)    sqrt(2) sqrt(3)
(%i7) length (vals[1]);
(%o7)                                  1
(%i8) for i thru length (vals[1]) do disp (val[i] = vals[1][i],  mult[i] = vals[2][i], vec[i] = vecs[i]);
val  = (vals )
1        1
1

mult  = (vals )
1        2
1

vec  = vecs
1       1

(%o8)                                done
(%i9) P2: matrix([0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0]);
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
(%o9)                  [                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
(%i10) ```
Run Example
```load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) P: matrix([0,1,0],[0,0,1],[1,0,0]);
[ 0  1  0 ]
[         ]
(%o2)                             [ 0  0  1 ]
[         ]
[ 1  0  0 ]
(%i3) Pdag: ctranspose(P);
[ 0  0  1 ]
[         ]
(%o3)                             [ 1  0  0 ]
[         ]
[ 0  1  0 ]
(%i4) A: P+Pdag;
[ 0  1  1 ]
[         ]
(%o4)                             [ 1  0  1 ]
[         ]
[ 1  1  0 ]
(%i5) hermitianmatrix: true;
(%o5)                                true
(%i6) [vals, vecs] = uniteigenvectors(A);
(%o6) [vals, vecs] = [[[2, - 1], [1, 2]],
1        1        1            1             1
[[[-------, -------, -------]], [[-------, 0, - -------],
sqrt(3)  sqrt(3)  sqrt(3)      sqrt(2)       sqrt(2)
1         sqrt(2)           1
[- ---------------, -------, - ---------------]]]]
sqrt(2) sqrt(3)  sqrt(3)    sqrt(2) sqrt(3)
(%i7) length (vals[1]);
(%o7)                                  1
(%i8) for i:1 thru length(vals[1]) do disp (val[i] = vals[1][i],  mult[i] = vals[2][i], vec[i] = vecs[i]);
val  = (vals )
1        1
1

mult  = (vals )
1        2
1

vec  = vecs
1       1

(%o8)                                done
(%i9) P2: matrix([0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0]);
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
(%o9)                  [                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
(%i10) ```

### Related Help

Help for Ctranspose

Help for Length

Help for Matrix

Help for True