2x2 Projection matrix of rank 1

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john 2022-11-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1860133-2x2-projection-matrix-of-rank-1

编辑： john 2022-11-27

采纳的回答： Matt J

在 MATLAB Online 中打开

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Rik 2022-11-24

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

john 2022-11-27

编辑：john 2022-11-27

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采纳的回答

Matt J 2022-11-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1860133-2x2-projection-matrix-of-rank-1#answer_1108998

编辑：Matt J 2022-11-23

在 MATLAB Online 中打开

a=[1; 2]; n=[3; 4]; x=[5; 6];
r1p(a,n,a)
ans = 2×1
    0.1789
    0.3578
r1p(a,n,n)
ans = 2×1
1.0e-15 *

   -0.1986
   -0.3972
r1p(a,n,x)
ans = 2×1
   -0.1789
   -0.3578
function p = r1p(a,n,x)
% computes the action of P, the 2x2 projection matrix of rank 1 having
% a - the sole basis vector for the column space of P
% n - the sole basis vector for the null space of P
    a = normalize(a(:),'n'); 
    b = normalize(null(n(:)'),'n');
    
    p = dot(x,b)*a;
end

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john 2022-11-23

Thank you so much for continuing to help me out. However, this now works for a=[1; 0.01]; n=[0.01; 1]; x=[1; 0]; (just have to negate it), but does not return the correct answer for a=[1; 2]; n=[3; 4]; x=[5; 6];

Matt J 2022-11-23

Again, you do not provide what you think is the correct answer, or an explanation of why that answer is correct..

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更多回答（1 个）

Moiez Qamar 2022-11-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1860133-2x2-projection-matrix-of-rank-1#answer_1110893

在 MATLAB Online 中打开

%should work for:
a=[1; 0.01]
a = 2×1
    1.0000
    0.0100
n=[0.01; 1]
n = 2×1
    0.0100
    1.0000
x=[1; 0]
x = 2×1
     1
     0
p=r1p(a,n,x)
P = 2×2
    1.0001   -0.0100
    0.0100   -0.0001
p = 2×1
    1.0001
    0.0100
p = 2×1
    1.0001
    0.0100
%and for:
a=[1; 0];  
n=[0; 1];  
x=[1; 0];
p = r1p(a,n,x); 
P = 2×2
     1     0
     0     0
p = 2×1
     1
     0
function p = r1p(a,n,x)
    % computes the action of P, the 2x2 projection matrix of rank 1 having
    % a - the sole basis vector for the column space of P
    % n - the sole basis vector for the null space of P
    xi=[0 -1; 1 0]*n;
    chi=xi/(xi'*a);
    P=a*chi'
    p=P*x
end