Jens Eising, Line\303\246r Algebra, Kapitel 8Preben Alsholm, 11/8 2008restart;with(LinearAlgebra):libname:="J:/DMat/libDMat",libname;with(DMat):Eksempel 8.5X,Y:=Vector(4,symbol=x),Vector(4,symbol=y);Transpose(X).Y;X.Y;DotProduct(X,Y);DotProduct(X,Y,conjugate=false);Norm(X,2,conjugate=false);Eksempel 8.11u1,u2,u3:=<2,2,4,1>,<0,0,-5,-5>,<5,3,3,-3>;GramSchmidt([u1,u2,u3]);GramSchmidt([u1,u2,u3],normalized=true);Eksempel 8.16A:=Matrix([[2,-2,1],[-2,5,-2],[1,-2,2]]);Eigenvectors(A);NullSpace(A-1);B1:=GramSchmidt(%,normalized=true);NullSpace(A-7);Vi opn\303\245r her en normalisering enten ved brug af Normalize (bem\303\246rk 2-tallet) eller ved brug af GramScmidt p\303\245 \303\251n vektor:Normalize(op(%),2);B2:=GramSchmidt(%%,normalized=true);Q:=Matrix([op(B1),op(B2)]);Transpose(Q).Q;Transpose(Q).A.Q;simplify(Determinant(Q));Eksempel 8.22A:=Matrix([[7,-2,0],[-2,6,-2],[0,-2,5]]);X:=Vector(3,symbol=x);K:=X->expand(Transpose(X).A.X);K(X);Lambda,V:=Eigenvectors(A);Q:=Matrix(map(Normalize,[Column(V,1..3)],2));Transpose(Q).A.Q;Y:=Vector(3,symbol=y);K(Q.Y);