Hello,
Thank you!1) Let be a unit vector. What is the meaning of the linear mapping , defined as
2) Which linear subspace is the best approximation to the set of points in the sense that the Euclidean distance to the subspace is minimized:
Hello,
Thank you!1) Let be a unit vector. What is the meaning of the linear mapping , defined as
2) Which linear subspace is the best approximation to the set of points in the sense that the Euclidean distance to the subspace is minimized:
1) The mapping A is the orthogonal projection onto the one-dimensional subspace spanned by the unit vector v.
2) So the unit vector v that minimises the expression spans a line (=one-dimensional subspace) that is the best approximation to the set of points in the sense that the mean of the squares of the Euclidean distances from the points to the line is minimised.