Sentence examples for operations of taking from inspiring English sources

The superscripts T, H, R, and I stand, respectively, for the operations of taking the transpose, Hermitian conjugate, complex conjugate, real part, and imaginary part.

In fact, the operations of taking ϱ -core and ϱ -neighbourhood do not commute: the equality in the inclusion ( D ϱ ⊂ D (15).

The sets that are obtained in a countable number of steps by starting from the basic open sets and applying the operations of taking the complement and forming a countable union of previously obtained sets are the Borel sets.

Two basic results are important here: (i) amenability of groups is preserved by the four operations of taking subgroups, quotients, directs limits, and extensions with amenable kernels (already in [123]), and (ii) groups of intermediate growth are amenable (this goes back to [3], and is also a straightforward consequence of Følner's Criterion [63]).

The operation of taking a rectangular window in each FFT frame results in a wide spectra.

This means that the operation of taking Cesàro means preserves convergent sequences and their limits.

The operation of taking tensor products T ⊗ S preserves many properties of T ∈ B ( H ) and S ∈ B ( K ), but by no means all of them.

Now consider the operation of taking the complement $\bar{R}$ of a given set $R$: the complement $\bar{R}$ contains exactly and all those $s$ that are not included in $R$.

end{aligned}When expressed with respect to compatible bases of V and (V^*), these maps are just the standard operation of taking the complex conjugate of the matrices of (mathsf {A}) and (mathsf {B}).

The equivariance property of (widetilde{psi }) follows from the fact that (g mapsto s g^dagger s) on (mathrm {Mp}) coincides with the operation of taking the inverse, (g mapsto g^{-1}).

The modified Cayley transformation intertwines the anti-holomorphic involution (psi :, h mapsto s h^dagger s) with the operation of taking the Hermitian conjugate (X mapsto X^dagger ): begin{aligned} a psi (h)) = a(h)^dagger.