Modify the attached code to implement vector projection.

attached code :

function y = proj(x, V)

% x (nx1): input vector

% V (nxk): matrix, whose column vectors are supposed to be orthonormal

% y (nx1): projection of x onto the span of the column vectors of V

x = [1; 2; 3];

V = [[1; 0; 0] [0; 1/sqrt(2); 1/sqrt(2)]];

y = zeros(size(x));

Question : How can i calculate this code? (y = proj(x, V))

I can't solve this problem... Isn't it using the dot product?

Answer 1

[Aditya]

Hi jaeuk,

I understand that you are looking to implement vector projection in MATLAB. The key is to use the dot product to project the vector x onto each orthonormal basis vector in V and sum these projections.

The modified code is as follows:

function y = proj(x, V) 
% x (nx1): input vector 
% V (nxk): matrix, whose column vectors are supposed to be orthonormal 
% y (nx1): projection of x onto the span of the column vectors of V 

% Initialize y as a zero vector of the same size as x 
y = zeros(size(x)); 

% Loop over each column vector in V 
for k = 1:size(V, 2) 
    % Calculate the projection of x onto the k-th column vector of V 
    y = y + (dot(x, V(:,k)) * V(:,k)); 
end 

To visualize this in a 3D space (for 3x1 vectors) for the attached example, you can use MATLAB's “plot3” function. However, for dimensions higher than three, a direct visual representation is not possible with “plot3”. In such cases, you may need to reduce the dimensionality for visualization or use alternative methods to represent high-dimensional data.

Hope this helps!