Moreover, U can be chosen to be a rotation matrix, as inverting an axis does not have any effect on N ( 0, Λ ), but inverting a column changes the sign of U's determinant.

Moreover, since composition of rotations corresponds to matrix multiplication, the rotation group is isomorphic to the special orthogonal group SO ( 3 ).

Moreover, D & C algorithms can be designed for important algorithms ( e. g., sorting, FFTs, and matrix multiplication ) to be optimal cache-oblivious algorithms – they use the cache in a provably optimal way, in an asymptotic sense, regardless of the cache size.

Indeed, the ( i, i ) entry of the product A adj ( A ) is the scalar product of row i of A with row i of the cofactor matrix C, which is simply the Laplace formula for det ( A ) expanded by row i. Moreover, for i ≠ j the ( i, j ) entry of the product is the scalar product of row i of A with row j of C, which is the Laplace formula for the determinant of a matrix whose i and j rows are equal and is therefore zero.

Moreover, computing the permanent of a 0-1 matrix ( matrix whose entries are 0 or 1 ) is # P-complete.

Moreover, a symmetric matrix A is uniquely determined by the corresponding quadratic form.

Moreover, the matrix coefficients of the irreducible unitary representations form an orthonormal basis of L < sup > 2 </ sup >( G ).

Moreover, Hardy briefly admitted that — just as the application of matrix theory and group theory to physics had come unexpectedly — the time may come where some kinds of beautiful, " real " mathematics may be useful as well.

Moreover, because fat grafts are biologically sensitive, they cannot survive in the empty implantation pocket, instead, they are injected to and diffused within the breast-tissue matrix ( recipient site ), replacing approximately 50 % of the volume of the removed implant — as permanent breast augmentation.

Moreover, for n < p, the empirical estimate of the covariance matrix becomes singular, i. e. it cannot be inverted to compute the precision matrix.

Moreover, the matrix v w < sup > T </ sup > is the projection onto the eigenspace corresponding to r. This projection is called the Perron projection.

Moreover the matrix v w < sup > t </ sup > is the spectral projection corresponding to r-Perron projection.

Moreover there exists a matrix M given below, such that M < sup > k </ sup > remains not positive ( just non-negative ) for all k < n < sup > 2 </ sup >- 2n + 2, in particular ( M < sup > n < sup > 2 </ sup >- 2n + 1 </ sup >)< sub > 11 </ sub >= 0.

Moreover, for every vector norm on, there exists a unique positive real number such that is a sub-multiplicative matrix norm for every.

Moreover, the law of the land is not irrevocable ; ;

Moreover its posture of stubborn but simple resistance is doomed to failure because of the metaphysical weakness of the existent form of order, once the activation of change has reached visible proportions.

Moreover, if the critic instructs his audience in what to see in a work, he is contributing to this pseudo-thinking ; ;

Moreover, the hearing officer's report is but intradepartmental, is directed to the Attorney General and, of course, is not the recommendation of the Department.

Moreover, the piece is written in five movements, rather than the conventional four of most quintets, and this gives the opus a serenade or divertimento flavor.

Moreover, it will be asymmetric until a certain critical Af distance is reached, below which it will become symmetric.

Moreover, the responsiveness of the hypothalamus to nociceptive stimulation is greatly increased under these conditions.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

Moreover, in this involution there is a cone of invariant lines of order Af, namely the cone of secants of **zg which pass through P.

Moreover, the current information on what types of training are needed and possible is too limited and fragmentary.

Moreover, the taunt concerning the `` sophisticated '' echelon and its alleged erudition is put to test during every campaign, and accrues only upon results ; ;

Moreover, it is likely that Federal policies aimed at stimulating a faster rate of economic growth of the country, to keep ahead of the Communist countries and to demonstrate that our free economic system is better than theirs, will lead to rising Federal spending in certain areas such as education, housing, medical aid, and the like.

Moreover, it is too readily forgotten that in the Republic what gave the initial impetus to Plato's excursus into the construction of an imaginary commonwealth with its ruling-class communism of goods, wives, and children, was his quest for a canon for the proper ordering of the individual human psyche ; ;

Moreover, the cost of operations is always high in any new store, as the conservative bankers who act as controllers for retail giants are beginning to discover.

Moreover, the President is meeting the Soviet leader at a time when the Administration has still not decided on the scope of America's firm foreign policy commitments.

Moreover, there is the 1908 theory that America derives from Richard Amerike of Bristol, England, financier of John Cabot's 1497 expedition.

Individuals who survived to this, the latest and highest stage of evolutionary progress would be “ those in whom the power of self-preservation is the greatest — are the select of their generation .” Moreover, Spencer perceived governmental authority as borrowed from the people to perform the transitory aims of establishing social cohesion, insurance of rights, and security.

Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by bit shifting.

Moreover they argued that some species have been created for the purpose of being sacrificed and eaten by humans, that it is normal for animals to kill and eat other animals, that agriculture, too, inevitably leads to the death of many animals, that plants are living beings as well and must still be destroyed, that we unintentionally and unknowingly destroy life forms all the time, and that a hunted animal has a fair chance to survive by killing the hunter.

Moreover, oxidative stress is both the cause and the consequence of disease.

Moreover, frequent smashing can be exhausting in singles where the conservation of a player's energy is at a premium.

Moreover, Frederick A. Tatford in Prophet of Edom ’ s Doom says that Obadiah ’ s prophecy is fulfilled today as there is currently no trace of anyone who may be identified as an Edomite.

Moreover, stated Day, `` He always omits facts which tend to disprove his hypothesis ''.

Moreover, the conclusions he draws from the findings are not always the only ones possible.

Moreover, by systematically varying the operating conditions in the first stage and always using the optimal Af-stage policy for the remaining stages, we shall eventually find the optimal policy for all R stages.

Moreover, nursing various Stubblefields -- her aunt, then her mother, then her father -- through their lengthy illnesses ( everybody could tell you the Stubblefields were always sick ), Theresa had had a chance to read quite a lot.

Moreover, foodservice establishments of this class would always have long term contracts with famous performers ( such as national treasure class performers ) to perform onsite, though not on a daily basis.

It would be in the forum or thereabouts that one would expect to find a medicus .” Moreover, he says that characters that oppose one another always have to exit in opposite directions.

Moreover, this separation of the rational self from the relentless " Beast " will, Trimpey says, enable addicts to always remain aware of the repercussions associated with a single relapse.

Moreover, there are a number of genera whose placement into the Caesalpinioideae is not always agreed on ( e. g. Dimorphandra ).

Moreover, because horn is always inedible, it is considered afra be-alma ( mere dust ) and not an unkosher substance.

Moreover, governmental policies toward investment were not always opposed to foreign capital: the Brazilian industrialization process was based on a tripod which involved governmental, private, and foreign capital, the first being directed to infrastructure and heavy industry, the second to manufacturing consumer goods, and the third, to the production of durable goods ( such as automobiles ).

Moreover, reverse engineering is not always able to reveal the differences between more-reliable and less-reliable diode laser products.

Moreover, this always leaves a one-piston gap between the piston on its combustion stroke and the piston on compression.

Moreover, good does not always vanquish evil in Leamas's world – an existential fact problematic to some conservative critics.

Moreover the addressee would not infrequently refuse a piece of mail, which then had to be taken back to the Post Office ( post office budgets always allowed for an appreciable volume of unpaid-for mail ).

Moreover, Kekkonen was unconvinced that Virolainen always supported his official foreign policy toward the Soviet Union.

Moreover, while the solutions to the original problem are always regular, it turns out that the solutions to the extended problem may have singularities if k ≤ n − 2.

Moreover, it was universally agreed by the punditry that the Liberals had controlled the agenda of the campaign, always keeping their three key issues: public automobile insurance, public health care and public power in the forefront of the agenda.

Moreover, actual contact is not always necessary ; I have had these sounds proceeding from the floor, walls, etc., when the medium's hands and feet were held – when she was standing on a chair-when she was suspended in a swing from the ceiling-when she was enclosed in a wire cage – and when she had fallen fainting on a sofa.

Moreover, both the name " GNU " and the name " Linux " are intentionally related to the name " Unix ", and Unix has always conceptually included the C library and userland tools as well as the kernel.

Moreover, their soil should always be moist.

Moreover, Bernardo has always claimed that, while he raped and tortured Leslie Mahaffy and Kristen French, it was Homolka who actually killed them.

Moreover, popular revolts almost always failed unless they had the support and patronage of the noble or gentry classes.

Moreover, the gerousia always had the power to veto the decision of the apella.

Moreover, even with regular use, effectiveness in prevention on dental trauma is not complete, and injuries can still occur even when mouthguards are used as users are not always aware of the best makes or size, which inevitably result in a poor fit.