Prajin Khadka

The Simplest Example of a Vector is x = [1 ,2 ]. It is a 2 element or 2-dimensional vector. The 2 elements can be taken as x and y, they are exactly the cartesian co-ordinates in a 2-d space. The vector corresponds to the point in that space. Vectors with n elements will represent points in d-dimensional space. Let's Visualize vector by plotting. We would be using python matpolitlib for plotting. The following pictures show the vector in a 2d space.  We can plot as many vectors in a 2d space with 2 elements, and there would be as many vectors in vector space. The Linear combination of these vectors falls on the same space, that is what we simply call vector space. Projection of Vector onto another Vector. In the following picture, what would be the projection of the Vector (Red) on Vector(blue) ? Visualize in your mind first. first, let's recall the formula of projection. The upper partis just the dot product and the lower part is the magnitude ...