Is there a matrix_element_inv in Maxima? - maxima

Question

In Maxima, we have matrix_element_add, matrix_element_mult and matrix_element_transpose.
Is there a matrix_element_inv, and if not, how could I make one?

Answer 1

If you want to invert matrix,first remember that not all matrix can be inverted, so first be sure that your matrix can be inverted.
For maxima working with matrix the operator for multiplying is .
so with A . A = A^2
if we want to get this value is A^^2
Normally the operator apply to each element of the matrix so if you would to invert all the elements:
(%i1) A: matrix ([17, 3], [-8, 11]);
[ 17 3 ]
(%o1) [ ]
[ - 8 11 ]
(%i9) A^-1;
[ 1 1 ]
[ -- - ]
[ 17 3 ]
(%o9) [ ]
[ 1 1 ]
[ - - -- ]
[ 8 11 ]
then to get the inverse of a matrix:
(%i2) B: A^^-1;
[ 11 3 ]
[ --- - --- ]
[ 211 211 ]
(%o2) [ ]
[ 8 17 ]
[ --- --- ]
[ 211 211 ]
(%i4) B.A;
[ 1 0 ]
(%o4) [ ]
[ 0 1 ]
(%i5) A.B;
[ 1 0 ]
(%o5) [ ]
[ 0 1 ]
be sure that your matrix is invertible:
(%i6) Bad: matrix ([2, 3], [4, 6]);
[ 2 3 ]
(%o6) [ ]
[ 4 6 ]
(%i7) Bad^^-1;
expt: undefined: 0 to a negative exponent.
-- an error. To debug this try: debugmode(true);
(%i8) newdet(Bad);
(%o8)/R/ 0
Now you should read carefully this section:
http://maxima.sourceforge.net/docs/manual/maxima_23.html
specially when telling about
matrix_element_add
so really there are only this opereators so doesn't exist a matrix_element_inv
so you can write your own using lambda functions as follows for example for getting the transpose of all the inverted elements:
(%i10) matrix_element_transpose: lambda ([x], x^-1)$
(%i11) transpose(A);
[ 1 1 ]
[ -- - - ]
[ 17 8 ]
(%o11) [ ]
[ 1 1 ]
[ - -- ]
[ 3 11 ]
hope this helps