Since these circular tubes were used to display rectangular images, the diagonal measurement of the rectangle was equivalent to the diameter of the tube's face.

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 equalizers may be constructed from pullbacks and binary products ( consider the pullback of ( f, g ) along the diagonal Δ ), a category is complete if and only if it has pullbacks and products.

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 most of the line is single track, the extra trains display a green disk with a diagonal white line on the front to indicate to station staff and signal operators that there is a train following in the same direction

Since D is diagonal, raising it to power, just involves raising each element on the diagonal to the power t. This is much easier to do and to understand than raising A to power t, since A is usually not diagonal.

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 these circular tubes were used to display rectangular images, the diagonal measurement of the rectangle was equivalent to the diameter of the tube's face.

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

Since the Poison Cards were no longer in play, a player could only lose by making a diagonal line.

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 we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since at a minimum the starting code address vector must always be valid on reset, systems commonly included some nonvolatile memory ( e. g. ROM ) starting at address zero to contain the vectors and bootstrap code.

Since this construction works for any vector space V, we conclude that T is a functor from K-Vect to K-Alg.

Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector.

Since the typical vector operation would involve loading a small set of data into the vector registers and then running several operations on it, the vector system of the new design had its own separate pipeline.

Since this is an electromagnetic wave each electric field vector has a corresponding, but not illustrated, magnetic field vector that is at a right angle to the electric field vector and proportional in magnitude to it.

Since the propagation vector is proportional to the photon's momentum, the transverse propagation direction must remain the same in both regions.

Since the Poynting vector only occurs in Poynting's theorem as a divergence ∇ • S, the Poynting vector S is arbitrary to the extent that one can add a curl of a field F to S,

Since elements of W are necessarily elements of V, axioms 1, 2 and 5-8 of a vector space are satisfied.

Since then, the supercomputer market has focused much more on massively parallel processing rather than better implementations of vector processors.

Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines.

Since the intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

Since all these values are distinct, this is usually done using a bit vector.

However, the more difficult proof of the converse ( see below ) makes use of the vector space structure: Since both of the factors are vector spaces over Q, the tensor product can be taken over Q.

Since version 3. 0, Leveller includes vector shapes, which can be used for both modeling and coloration.

The set of ( p < sub > i </ sub >, n < sub > i </ sub >) is thus a sampling of a continuous vector field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may or may not have a solution: the necessary and sufficient condition for a smooth vector field V to be the gradient of a function f is that the curl of V must be identically zero.

Since 1944 he has also conducted regularly at the San Francisco Opera, where he made his debut with a memorable performance of Verdi's Falstaff.

Since 1954 the Negro's desire for social justice has led to an ironically anarchical rebellion.

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 1953 California has led the nation in enacting guarantees that public business shall be publicly conducted, but not until this year did the lawmakers in Sacramento plug the remaining loopholes in the Brown Act.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since it was issued in the spring of 1611, the King James Version has been most generally considered the most poetic and beautiful of all translations of the Bible.

Since the Connally amendment has the effect of giving the same right to the other party to a dispute with the United States, it also prevents us from using the court effectively.

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 then nothing has happened to save the life of Pope.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since then, there has been a notable increase in the number of stations and also the accumulation of additional data and the development of new techniques for using it, leading to a better understanding of propagation phenomena.

Since the Industrial Revolution, when factories emerged, this classical pattern has been followed.

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

Since the course, one member has lost her husband.

Since her bereavement this individual has reported to the writer on numerous occasions about how helpful the class discussions were to her in this adjustment crisis.

Since on the one hand school desegregation has come in Virginia hand-in-glove with pupil assignment, shall we support the plan??

Since this book is concerned only incidentally with railroad rates, it will not attempt to analyze the methods by which the staff of the Interstate Commerce Commission has estimated out-of-pocket costs and apportioned residue costs.

Since that time the telegraph office has shifted in location from the railroad station at the Depot and shops at the Center back to the town clerk's office and drugstore at the Village.

Since 1948 the working headquarters has been the Department of Geology and Mineralogy.

Since the removal force is a function of coating thickness, a differential transformer pickup has been incorporated into the instrument to accurately measure film thickness.

Since the mid 1950s, when urethane foam first made its appearance in the American market, growth has been little short of fantastic.

Since interviewing is the basic therapeutic and diagnostic instrument of modern psychiatry, the recording of interviews for playbacks and study has been a boost of Redstone proportions in new research and training.

Since 1949, the St. Louis club has been below on May 1 just four times.

Since 1927, fewer than a dozen men have made serious runs at Babe Ruth's record and each, in turn, has been thwarted.