jacobian2by2 - Y=[p q;r/p det(X/p J=jacobian(Y,X JAC_lu...

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%jacobian2by2.m %Code 8.1 of Random Eigenvalues by Alan Edelman %Experiment: Compute the Jacobian of a 2x2 matrix function %Comment: Symbolic tools are not perfect. The author % exercised care in choosing the variables. syms p q r s a b c d t e1 e2 X=[p q ; r s]; A=[a b;c d]; %% Compute Jacobians Y=X^2; J=jacobian(Y(:),X(:)), JAC_square =factor(det(J)) Y=X^3; J=jacobian(Y(:),X(:)), JAC_cube =factor(det(J)) Y=inv(X); J=jacobian(Y(:),X(:)), JAC_inv =factor(det(J)) Y=A*X; J=jacobian(Y(:),X(:)), JAC_linear =factor(det(J))
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Unformatted text preview: Y=[p q;r/p det(X)/p]; J=jacobian(Y(:),X(:)), JAC_lu =factor(det(J)) x=[p s r];y=[sqrt(p) sqrt(s) r/(sqrt(p)*sqrt(s))]; J=jacobian(y,x), JAC_DMD =factor(det(J)) x=[p s]; y=[ atan(p/s) sqrt(p^2+s^2)]; J=jacobian(y,x), JAC_notrace =factor(det(J)) Q=[cos(t) -sin(t); sin(t) cos(t)]; D=[e1 0;0 e2];Y=Q*D*Q.'; y=[Y(1,1) Y(2,2) Y(1,2)]; x=[t e1 e2]; J=jacobian(y,x), JAC_symeig =simplify(det(J)) X=[p s;s r]; Y=A.'*X*A; y=[Y(1,1) Y(2,2) Y(1,2)]; x=[p r s]; J=jacobian(y,x), JAC_symcong =factor(det(J))...
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