### The Maxima on-line user's manual

Algebra Calculator

#### Determinant

Function: determinant (<M>) Computes the determinant of <M> by a method similar to Gaussian elimination.

The form of the result depends upon the setting of the switch `ratmx`.

There is a special routine for computing sparse determinants which is called when the switches `ratmx` and `sparse` are both `true`.

```(%o1)                                true
(%i2) ```

### Related Examples

M:matrix([0.8, 0.2, 0...

determinant(M);

X:matrix([x],[y],[z]);

Calculate

##### determinant-matrix

determinant(matrix([-...

Calculate

##### determinant-matrix-permanent

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

permanent(a);

determinant(a);

Calculate

##### determinant-matrix

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

dA:determinant (A);

Calculate

##### determinant-matrix

A: matrix([1,3,2],[1,...

determinant(A);

Calculate

##### determinant-euler-matrix

a:matrix([a,b],[c,d]);

b:matrix([3,0],[0,8]);

a.b.a^(-1);

Calculate

mx:1;

my:0;

mz:2;

Calculate

##### determinant-expand-jacobian

H:[x1*x4,x2*x4,x3*x4,...

JH:jacobian(H,[x1,x2,...

expand(determinant(JH));

Calculate

##### determinant-diff-hessian-matrix

f(x,y):=(a*x^2 + b*x*y);

xx:diff(diff(f(x,y),x...

xy:diff(diff(f(x,y),x...

Calculate

##### determinant-diagmatrix-matrix-modulus-solve-triangularize

modulus:11;

M: matrix ([7, 3, 4, ...

determinant(M);

Calculate