Sentence examples for of orthogonal projections from inspiring English sources

Our result gives a Schur Horn theorem for operators with three point spectrum analogous to Kadisonʼs Pythagorean theorem and carpenterʼs theorem, which characterize the diagonals of orthogonal projections.

The identity in ℳ is denoted by 1, and we denote by M proj the lattice of (orthogonal) projections in ℳ.

We study the set Pcc of orthogonal projections P in H which essentially commute with E+ (or equivalently with E−), i.e.[P,E+]= PE+−E+Pis compact.

and this in turn is equivalent to the existence of a set of orthogonal projections Rα1...αiti (for any ti≤tn) that extend consistently the given set of histories and are perfectly correlated with the histories of the original set (Gell-Mann and Hartle 1990).

Let P be the orthogonal projection on ({mathrm{ran}}(Pi )) and Q the orthogonal projection onto ({mathrm{ran}}({varvec{1}}-Pi )) (P and Q must obey (ker (P cap ker (Q) = ker 1-P capp ker (1-P cap}) and every such pair of orthogonal projections corresponds to an oblique projection (Pi )).

A sequence ({x_{n}}), generated by the formula x_{n+1}=P_{C}bigl(x_{n}-lambda_{n}A^ I-P_{Q})Ax_{n}-lambda_{n}A^ I-P_{ngeq0, (1.2) where the parameters (lambda_{n}in(0,frac{2}{|A|^{2}})), (P_{C}: Hrightarrow C), and (P_{Q}: H rightarrow Q), is a set of orthogonal projections.

In both these cases, the Gamma-kernel induces an operator of orthogonal projection acting in (L_2({mathbb {Z}}^{prime })).

Let (Pi (x,y)) be a kernel yielding an operator of orthogonal projection acting in (L_2({mathbb Z})).

While the variational theory of boundary value problems has its starting point in the method of orthogonal projection, the theory of variational inequalities has its starting point in the projection on a convex set.

A method for quantitative analysis of diclofenac sodium powder on the basis of near-infrared (NIR) spectroscopy is investigated by using of orthogonal projection to latent structures (O-PLS) combined with artificial neural network (ANN).

Let (mu ) be a (sigma )-finite Borel probability measure on (mathbb {R}), and let (Pi (x,y)) be the kernel of a locally trace-class operator of orthogonal projection acting in (L_2(mathbb {R}, mu )).