Using matlab to find vectors that are orthogonal to another vector.

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Lee Ming De 2019-11-7

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https://ww2.mathworks.cn/matlabcentral/answers/489674-using-matlab-to-find-vectors-that-are-orthogonal-to-another-vector

编辑： David Goodmanson 2023-5-10

Is there a way that matlab can be used to find a general solution for vectors that are orthogonal to another vector. (eg, (1,1) )? Without using matlab, i can get the general solution which is x =-y, but i cant find a way to do this using matlab.

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Answer 1

Jan 2019-11-7

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https://ww2.mathworks.cn/matlabcentral/answers/489674-using-matlab-to-find-vectors-that-are-orthogonal-to-another-vector#answer_400301

编辑：Jan 2019-11-7

Do you mean 2D vectors?

v  = rand(1, 2)   % Any test vector
vp = [-v(2), v(1)]
dot(v, vp)        % Orthogonal means: dot product is 0

So "x=-y" is a part of the solution. Add "y=x" and you get one of the two perpendicular vectors. -vp is the other one.

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Oghenetega Oguns 2023-5-9

What about when the vector is 3D?

Thanks

David Goodmanson 2023-5-10

编辑：David Goodmanson 2023-5-10

Hi O^2,

n = 5;
v = rand(n,1)
% make sure that v is a row vector, just in case it was a column vector
v = v(:).'
%  find a set of n-1 mutually orthogonal column vectors
%  that are all perpendicular to v.
n = null(v)           