### Related

##### function-numer-sqrt

f(x):=x^307-7*x^37+3*...

a=(1-%i*sqrt(3))/2;

f(a),numer;

Calculate

aa : matrix([a,b],[c,...

mat_function(exp,aa);

Calculate

? function;

Calculate

##### function-limit

function: limit((ln(1...

Calculate

##### function-log-taylor

k: 1-eps;

function: -( 1-k^2 + ...

taylor( function, eps...

Calculate

##### function

value : 3;

equation : a+2=b;

function(x) := x+3;

Calculate

##### function

value : 3;

equation : a+2 =b;

function(x) := x + 3;

Calculate

##### function

value : 3;

equation : a+2=b;

function(x) := x+3;

Calculate

##### function-kill

value : 3;

equation : a+2=b;

function(x) := x+3;

Calculate

##### function-hessian

-- function: hessian;

Calculate

### function

Run Example
```(%i1)A:matrix([10, 4, 13], [5, 3, 7], [-9, -4, -12]);
[ 10    4    13  ]
[                ]
(%o1)                         [  5    3    7   ]
[                ]
[ - 9  - 4  - 12 ]
(%i2) b(t):=matrix([t],[0],[0]);
(%o2)                    b(t) := matrix([t], [0], [0])
(%i3) [vals,vecs] : eigenvectors(A);
1
(%o3)        [[[- 1, 1], [1, 2]], [[[1, -, - 1]], [[1, 1, - 1]]]]
2
(%i4) vals[1][2];
(%o4)                                  1
(%i5)  B: A-vals[1][2]*ident(3);
[  9    4    13  ]
[                ]
(%o5)                         [  5    2    7   ]
[                ]
[ - 9  - 4  - 13 ]
(%i6) nullity(B);
(%o6)                                  1
(%i7) nullity(B^^2);
(%o7)                                  2
(%i8) nullspace(B^^2);
[  0   ]  [  8   ]
[      ]  [      ]
(%o8)                      span([ - 24 ], [ - 16 ])
[      ]  [      ]
[  8   ]  [  0   ]
(%i9) define(psi(t),ratsimp(mat_function(exp,t*A)));
[ 10 t    4 t    13 t  ]
[                      ]
(%o9)        psi(t) := mat_function(exp, [  5 t    3 t    7 t   ])
[                      ]
[ - 9 t  - 4 t  - 12 t ]
(%i10) ```
Run Example
```-- function: hessian;
(%o1)                               hessian
(%i2) ```
Run Example
```RESPONSE : [-1];
(%o1)                                [- 1]
(%i2) LONCAPALIST: [2, 8/5, 3/2];
8  3
(%o2)                              [2, -, -]
5  2
(%i3) x: RESPONSE[1];
(%o3)                                 - 1
(%i4) function: [sin(LONCAPALIST[2]*x+LONCAPALIST[3]), cos(LONCAPALIST[2]*x+LONCAPALIST[3])];
1        1
(%o4)                        [- sin(--), cos(--)]
10       10
(%i5) func: function[LONCAPALIST[1]];
1
(%o5)                               cos(--)
10
(%i6) is(equal(0,func));
(%o6)                                false
(%i7) ```

### Related Help

Help for Function