Re: Obtaining the coefficient matrix of multivariable homogeneous linear equation system.

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Nov 18, 2022 at 10:36:34AM +0800, Hongyi Zhao wrote:
> But I still have some further minor questions:
> 
> 1. How to reshape the above output so that it can be feed to matker
> directly, as follows:

Do as told in linear algebra course:
Choose a basis and apply your linear function to all elements of the basis.

That is instead of 
? trmat=[x1,x2;x3,x4];A=[a,b;c,d];
? A * trmat - trmat *A

do

? A     = [a,b;c,d];
? basis = [matrix(2,2,k,l,k==i&&l==j)|i<-[1..2];j<-[1..2]]
%2 = [[1,0;0,0],[0,1;0,0],[0,0;1,0],[0,0;0,1]]
? C     = [A * B - B * A  | B<-basis]
%3 = [[0,-b;c,0],[-c,a-d;0,c],[b,0;-a+d,-b],[0,b;-c,0]]
? D     = Mat([concat(Vec(c))  | c<-C]~)
%4 = [0,-c,b,0;-b,a-d,0,b;c,0,-a+d,-c;0,c,-b,0]
? matker(D)
%5 = [1/c*a-d/c,1;1/c*b,0;1,0;0,1]

Cheers,
Bill.