Since entries may have multiple ObjectClasses values, each entry has a complex of optional and mandatory attribute sets formed from the union of the object classes it represents.

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Since the encyclopedia was first published starting in 1907 and has never been updated, many of its entries may be out of date either with respect to the wider culture or to the Catholic ecclesiastical world.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 was not introduced in the transformation and accordingly not in the Jacobian, it follows that does not depend upon and that is a sufficient statistics for.

In the case that V is a non-singular algebraic curve and i = 1, H < sup > 1 </ sup > is a free Z < sub > l </ sub >- module of rank 2g, dual to the Tate module of the Jacobian variety of V, where g is the genus of V. Since the first Betti number of a Riemann surface of genus g is 2g, this is isomorphic to the usual singular cohomology with Z < sub > ℓ </ sub > coefficients for complex algebraic curves.

Since it also includes the theory of the Jacobian variety of an algebraic curve, the study of this functor is a major issue in algebraic geometry.

Since there are only four distinct eigenvalues for this matrix, they have some multiplicity.

Since the above is a linear system of equations ( more technically a linear transformation ), they can be written in matrix form:

Since the gels are fragile and the probes are unable to enter the matrix, the RNA samples, now separated by size, are transferred to a nylon membrane through a capillary or vacuum blotting system.

Since the column vectors of A are the row vectors of the transpose of A ( denoted here by A < sup > T </ sup >), column rank of A equals row rank of A is equivalent to saying that the rank of a matrix is equal to the rank of its transpose, i. e. rk ( A ) = rk ( A < sup > T </ sup >).

Since the 1990s, many physicists believe that 11-dimensional M-theory, which is described in many sectors by matrix string theory, in many other sectors by perturbative string theory, is the theory of everything.

Since the kth leading principal minor of a triangular matrix is the product of its diagonal elements up to row k, Sylvester's criterion is equivalent to checking whether its diagonal elements are all positive.

Since matrix schemes follow the same laws of geometric progression as pyramids, they are subsequently as doomed to collapse.

Since the head is facing a different direction, the rotation matrix would be popped off the top of the stack and a different rotation matrix about the y-axis with a different angle would be pushed.

Since it was quite easy to stack interconnections ( wires ) inside the embedding matrix, the approach allowed designers to forget completely about the routing of wires ( usually a time-consuming operation of PCB design ): Anywhere the designer needs a connection, the machine will draw a wire in straight line from one location / pin to another.

Since is a rotation matrix its inverse is its transpose.

Since W ( by definition of the SVD of a real matrix ) is an orthogonal matrix, each row of Y < sup > T </ sup > is simply a rotation of the corresponding row of X < sup > T </ sup >.

Since < math > b_j < p </ math >, the elements of matrix are no other than the set of numbers:

Since an elementary reflection in the form of a Householder matrix can reduce any orthogonal matrix to this constrained form, a series of such reflections can bring any orthogonal matrix to the identity ; thus an orthogonal group is a reflection group.

Since shorter strands of DNA move through the gel matrix faster they are detected sooner and there is then a direct correlation between length of DNA strand and time at the detector.

Since the eigenvalues of this matrix coincide with the roots of the polynomial, one can use any eigenvalue algorithm to find the roots of the polynomial.

Since a shape memory polymer resin is used as the matrix, these composites have the ability to be easily manipulated into various configurations when they are heated above their activation temperatures and will exhibit high strength and stiffness at lower temperatures.