|Bill Allombert on Fri, 18 Nov 2022 12:22:01 +0100|
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|Re: Obtaining the coefficient matrix of multivariable homogeneous linear equation system.|
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.