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The Maxima on-line user's manual

Algebra Calculator

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Invert

Function: invert (<M>) Returns the inverse of the matrix <M>. The inverse is computed by the adjoint method.

m:matrix([1,2,3],[4,7,9]);
m2:submatrix(m,3);
m3:submatrix(1,m);
transpose(m);
invert(m2);
determinant(m2);
m2.invert(m2);
ident(2);
rank(m);
eigenvalues(m2);
eigenvectors(m2);
m2.invert(m2)-ident(2)

This allows a user to compute the inverse of a matrix with bfloat entries or polynomials with floating pt. coefficients without converting to cre-form.

Cofactors are computed by the determinant function, so if ratmx is false the inverse is computed without changing the representation of the elements.

The current implementation is inefficient for matrices of high order.

When detout is true, the determinant is factored out of the inverse.

The elements of the inverse are not automatically expanded. If <M> has polynomial elements, better appearing output can be generated by expand (invert (m)), detout. If it is desirable to then divide through by the determinant this can be accomplished by

     xthru (%) or alternatively from scratch by

expand (adjoint (m)) / expand (determinant (m)) invert (m) := adjoint (m) / determinant (m)

See ^^ (noncommutative exponent) for another method of inverting a matrix.

There are also some inexact matches for invert. Try ?? invert to see them.

(%o1)                                true
(%i2) 

Related Examples

invert-jacobian

A: jacobian ([a*If*Sh...

B: jacobian ([gh*Ih, ...

C: invert (B);

Calculate

invert-matrix

A:matrix([a,b,c],[d,e...

invert(A);

Calculate

invert-matrix

x:matrix([1,2,3],[4,7...

invert(x);

Calculate

invert-matrix

t:matrix([0,0,1],[1/2...

i:invert(t);

d0:matrix([1/2,0,0],[...

Calculate

invert-matrix

m1: matrix([1,0,0],[0...

A: matrix([2,4,-5],[0...

m2: invert(m1);

Calculate

invert-matrix

r1:[3,-5];

r2:[2,7];

r3:[8/31,3/31];

Calculate

invert-matrix

matrix([1,0,0],[0,-1,...

invert(matrix([1,0,of...

Calculate

invert-matrix

M:matrix([0,1/4,0],[1...

P:matrix([1,1,1],[-2,...

invert(P);

Calculate

invert-matrix

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

MI:invert(M);

MI*matrix([17,15,29],...

Calculate

invert-matrix

a: matrix([1, 2], [5,...

invert(a);

b:matrix([s, 0], [0, ...

Calculate