Sentence examples for sum of projections from inspiring English sources

We obtain a special operator matrix representation and some necessary/sufficient conditions for an infinite-dimensional operator to be expressible as a sum of projections.

We prove that a positive operator with essential norm strictly greater than one is always a sum of projections, and if an injective operator of the form I+K, where K is compact, is a sum of projections, then either traceK+= traceK−="∞ or K is of trace class with trace K a nonnegative integer.

The spectral theorem for compact self-adjoint operators on a Hilbert space H states that H splits into an orthogonal direct sum of the eigenspaces of an operator, and also gives an explicit decomposition of the operator as a sum of projections onto the eigenspaces.

The closure of the set of sums of projections is also characterized.

and V_{j - 1}^{M} = V_{j}^{M} oplus W_{j}^{M}, (35). the orthogonal projection of input signal x on (V_{j-1}^{M}) can be decomposed as the sum of orthogonal projections on (V_{j}^{M}) and (W_{j}^{M}).

The sum of all projections was set in relation to the total length of the regression line.

The percentage of direct bone implant contact was defined as the sum of these projections divided by the circumference of the specimen (Fig.  3).

A consequence of this scheme is that, usually, the sum of the projections onto all sub-systems does not completely recover the full density of states (cf. Figure 3).

(F ) Summed power of projections from the C1 map along 360 different directions normal to its helical axis.

The visual hull in (1) is defined as the sum of the projection areas of using.

The geometric error is the sum of the projection error in each camera view for a pair of correspondence points.