Since the entries of the Jacobian matrix are partial derivatives, we may simplify the above formula to get:

Since the product of diagonal matrices amounts to simply multiplying corresponding diagonal elements together, the power k of a diagonal matrix A will have entries raised to the power.

Since any algorithm for multiplying two n × n-matrices has to process all 2 × n < sup > 2 </ sup >- entries, there is an asymptotic lower bound of operations.

Since the entries of the matrix are ( linear or constant ) polynomials in λ, the determinant is also a polynomial in λ.

Since B is also a matrix with polynomials in t as entries, one can for each i collect the coefficients of in each entry to form a matrix B < sub > i </ sub > of numbers, such that one has

Since that time the ISC has expanded its monitoring operations ; its website cites a figure of over twenty million " intrusion detection log entries " per day.

Since memory addresses were stored in 16 bits, a 64K program was often a giant monster RPG screen program with 3, 000 lines of code, five or six files, and forty-odd array / table entries.

Since U is similar to A, it has the same multiset of eigenvalues, and since it is triangular, those eigenvalues are the diagonal entries of U.

Since for any triangular matrix A the matrix, whose determinant is the characteristic polynomial of A, is also triangular, the diagonal entries of A in fact give the multiset of eigenvalues of A ( an eigenvalue with multiplicity m occurs exactly m times as diagonal entry ).

Since then, she has shared the existence of this interdimensional blog to some of her closest family and friends, some of whom have also posted comments ( though only Lindesfarne herself posts main entries ).

Since the encyclopedia was first published starting in 1907 and has never been updated, many of its entries may be out of date either with respect to the wider culture or to the Catholic ecclesiastical world.

Since it covers the planet and not merely Oz, the Book's entries are compressed and sometimes cryptic, and difficult to decipher ( as in Paradox in Oz or Queen Ann in Oz ).

Since the actual sequence and the representative sequence are in the same equivalence class, their entries are the same after finitely many prisoners.

" Since then, its format has shifted often, from actual diary format entries to postings consisting simply of lists.

Since a given vector v is a finite linear combination of basis elements, the only nonzero entries of the coordinate vector for v will be the nonzero coefficients of the linear combination representing v. Thus the coordinate vector for v is zero except in finitely many entries.

* Since the diagonal entries of C and S are positive, S cannot be negative definite or negative semidefinite.

: Since each piece of advice is itself a procedure, it has its own entries and exits.

Since its inception it has attracted over 1, 000 entries yearly and has attracted over 60, 000 visitors every year.

" Since then I have published more than 5, 300 entries covering topics such as breast milk pumps, golf cart rides with Norah Jones, and the one guy I dated who talked like Elmo during sex.

Since then, the phrase has appeared in numerous forms: on T-shirts, on the Internet ( particularly in blog entries ), as a 2005 Seattle band name, and referenced in the " System Administrator Appreciation Day " song by Canadian comedy troupe Three Dead Trolls in a Baggie (" He's the only one in the building who knows what ' PC LOAD LETTER ' means.

Since 1970, he has written numerous articles and essays on theological and ecumenical subjects, including four entries in the Dictionary of the Ecumenical Movement ( WCC Publications, 1991 ), for which he was also a member of the editorial board.

Since 1983 he has been editing the German " Schach-Kalender ", a pocket-calendar with about 1200 biographical player entries each year and a lot of information, stories, anecdotes, statistics, pictures and other things each year.

Since the one-dimensional representations of B correspond to the representations of the diagonal matrices, with non-zero complex entries z and z < sup >− 1 </ sup >, and thus have the form

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since he had gross income of $600 or more, he must file a return in which he may claim an exemption deduction of $600.

Since you contributed more than half of his support, you may also claim an exemption for him on your return.

Since the latter obviously require an audacity you do not possess, you may perhaps suppose that I am taunting you as socially inferior.

Since electrical stimulation of the posterior hypothalamus produces the effects of wakefulness while stimulation of the anterior hypothalamus induces sleep, it may be said that the reactivity of the whole organism is altered by a change in the autonomic reactivity of the hypothalamus.

Since the details of the elections were settled the change of government had no direct effect on the technical aspects of the elections, and may have been more important as an indication of royal displeasure with the U.N.F.P.

Since writing was practiced in the Aegean before the end of the century, we may hope that the details of tradition will now be occasionally useful.

Since we are considering here relatively small diameter ( 1 - 1.5 inches ) fiber plates, their average thickness can be kept below 1/4 inch and their internal losses may be assumed as 15 percent ( per plate ).

Since by the principle of optimality the remaining stages use an optimal Af-stage policy with respect to Af, we may enter section Af of the table at this state Af and read off the optimal policy for stage Af and the resulting state Af.

Since these electrons are moving like planets, you may wonder whether there is an atomic sun at the center of the atom.

Since amateurs often do not have formal training, some amateur work may be considered sub-par.

Since the time of Catherine II the ranks of Abbot and Archimandrite have been given as honorary titles in the Russian Church, and may be given to any monastic, even if he does not in fact serve as the superior of a monastery.

Since various Molly Pitcher tales grew in the telling, many historians regard Molly Pitcher as folklore rather than history, or suggest that Molly Pitcher may be a composite image inspired by the actions of a number of real women.

Since the reference model given for traffic policing in the network is the GCRA, this algorithm is normally used for shaping as well, and single and dual leaky bucket implementations may be used as appropriate.

Since the 2002 edition, the Apostles ' Creed is included in the Roman Missal with the indication, " Instead of the Niceno-Constantinopolitan Creed, especially during Lent and Easter time, the baptismal Symbol of the Roman Church, known as the Apostles ’ Creed, may be used.

Since the Universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not had time to reach us.

Since the shields were wooden, they may have provided sufficient buoyancy

Since 1974, it has been a purely ceremonial style granted by royal charter to districts which may consist of a single town or may include a number of towns or rural areas.

Since the award criteria state that the Bronze Star Medal may be awarded to " any person ... while serving in any capacity in or with " the U. S. Armed Forces, awards to members of foreign armed services serving with the United States are permitted.

Since most Western economies are now considered " open " with free capital movement, this essentially means that central banks may target interest rates or exchange rates with credibility, but not both at once.

Since water that flows through a cave eventually comes out in streams and rivers, any pollution may ultimately end up in someone's drinking water, and can even seriously affect the surface environment, as well.