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!
