Furthermore, it is a general fact about conditional expectations that if " F " is any sub-" ? "-algebra of ? then the orthogonal projection
42.
Let H : \ mathcal E ^ \ bullet \ rightarrow \ mathcal H be the orthogonal projection, and let " G " be the Green's operator for ?.
43.
3-dimensional orthogonal projections can also be made with three orthonormal basis vectors, and displayed as a 3d model, and then projecting a certain perspective in 3D for a 2d image.
44.
The advantage of using orthogonal projection is that e _ \ min can be determined for use in the "'polynomial least squares "'processed statistical variance of the estimate.
45.
Pick a point in the unit sphere, " v ", so that orthogonal projection of the link to the plane perpendicular to " v " gives a link diagram.
46.
The least-squares estimator is simply an estimation of an orthogonal projection, using the Euclidean scalar product in \ mathbb { R } ^ n instead of the one defined for random variables.
47.
It coincides with the real part of the orthogonal projection ? 1 of ? 1 ? onto " H " 1 for the complex inner product on " H ".
48.
Each source signal can be extracted from a set of signal mixtures by taking the inner product of a weight vector and those signal mixtures where this inner product provides an orthogonal projection of the signal mixtures.
49.
For " N " > " J ", orthogonal projection yields the standard overdetermined system of equations ( often called normal equations ) used to compute the coefficients in the polynomial approximation.
50.
Obviously an orthogonal projection will, in general, reduce the average distance between points, but the lemma can be viewed as dealing with " relative distances ", which do not change under scaling.
