Sentence examples for matrices of pure from inspiring English sources

Then (a) the group K acts via its adjoint action transitively on the set of all skew-symmetric covariance matrices of pure quasifree states (whose singular values are all 1) and (b) the quasifree system is pure-state controllable if its system algebra is conjugate under SO ( 2 d ) to.

Let us now recall another result related to the singular values of the covariance matrices of pure quasifree states (Theorem 6.2 in [58], and Lemma 1 in [60]): Proposition 19 A quasifree state ρ is pure iff the following (equivalent) conditions hold for its covariance matrix G ρ : (a) The rows (and columns) of G ρ are real unit vectors which are pairwise orthogonal to each other.

As seawater freezes and ice forms, liquid brine and air are trapped within a matrix of pure ice crystals.

The volume fraction of non-conducting phase, namely equiaxed or angular alumina particles of various sizes and size-distributions embedded in a matrix of pure aluminum, is varied between 40 and 70 vol.-%.

In this case, we consider that, because of the chemical nature of the copolymer, the higher affinity of chloroform for CL than for LA (as obtained by the solubility parameters calculated by the Hoftyzer and van Krevelen theory [24]) has favored the phase separation of CL-enriched domains in a matrix of pure LA or of LA with a lower CL content.

For example, the Hankel matrix of a pure exponential is rank 1, while the one of a pure sinusoids or an exponentially damped sinusoid is rank -2.

It follows from Proposition 19(b) that the skew-symmetric covariance matrix of a pure quasifree state can be written as G ρ = ( 0 v 1 t − v 1 A 1 ), where v 1 denotes a normalized ( 2 d − 1 ) -dimensional vector and A 1 denotes a ( 2 d − 1 ) × ( 2 d − 1 ) -dimensional skew-symmetric matrix.

For example, if the values of the elements in the Mueller matrix of a pure retarder with retardance δeff and orientation θeff are large, then the symmetry in Eq. (16) will be more manifest, yielding lower ASD [ 21].

Mueller matrix of a pure retarder has non-zero values for the 9 lower right corner elements [ 20]; as such, these elements are more correlated to birefringence even in a turbid medium.

Al-based metal matrix composites consisting of pure Al reinforced with different amounts of mechanically alloyed Zr57Ti8Nb2.5Cu13.9Ni11.1Al7.5 glassy powder were produced by powder metallurgy, and their mechanical properties were investigated by room temperature compression tests.

The ablated surface of the carbon matrix for pure carbon/carbon composites was very smooth and glossy, while that for doped carbon/carbon composites was honeycombed and dim.