... the space Any vector in the space can be specified as one and only one combination of the basis vectors Any linearly independent set of vectors can be extended to a basis by adding (linearly independent) ... vector y onto the vector x We may also be interested in the projection of a point y onto a subspace For instance, we may want to project the point onto the plane defined by two vectors, or an ... impossible to have more than n orthonormal vectors in an n-dimensional space For instance, in three dimensions, one can only have vectors which are orthogonal, and thus, only three vectors can be...