Projection of Ax on By where norm(x)=norm(y)=1 and A,B are matrices.

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Ahsan Razaq
Ahsan Razaq 2023-5-17
评论： Ahsan Razaq 2023-5-17
I know how to project a vector x on vector y. But I would like to know if there is a function that could help me by projecting on where A and B are matrices and ∀ .
In other words, how can I get vectors of norm 1.

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Torsten
Torsten 2023-5-17
移动：Torsten 2023-5-17
The projection of A*x on B*y is
dot(A*x,B*y)/dot(B*y,B*y)*B*y
I don't know where you want norm = 1 come into play here.
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Torsten
Torsten 2023-5-17
编辑：Torsten 2023-5-17
Npoints = 100;
Ndim = 4; % points in a circle. ergo, easy to plot.
x = randn(Npoints,Ndim); % A normal dist is symmetrical
x = x./sqrt(sum(X.^2,2)); % project to the surface of the Ndim-sphere
x

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