# Orthogonal Sentence Examples

Such a determinant is of importance in the theory of

**orthogonal**substitution.We may therefore form an

**orthogonal**transformation in association with every skew determinant which has its leading diagonal elements unity, for the Zn(n-I) quantities b are clearly arbitrary.This is called the direct

**orthogonal**substitution, because the sense of rotation from the axis of X i to the axis of X, is the same as that from that of x i to that of x 2.In both cases the solution can be made

**orthogonal**to any number of specified functions.**Orthogonal**System.-In particular, if we consider the transformation from one pair of rectangular axes to another pair of rectangular axes we obtain an**orthogonal**system which we will now briefly inquire into.Clerk Maxwell, who showed amongst other things that a reciprocal can always be drawn to any figure which is the

**orthogonal**projection of a plane-faced polyhedron.If we project both polyhedra orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are

**orthogonal**instead of parallel.It may denote a simultaneous

**orthogonal**invariant of forms of orders n i, n2, n3,...; degree 0 of the covariant in the coefficients.The curves 0 = constant and 4, = constant form an

**orthogonal**system; and the interchange of 0 and 4, will give a new state of uniplanar motion, in which the velocity at every point is turned through a right angle without alteration of magnitude.Thus for m =2, the spheres are

**orthogonal**, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.AdvertisementThe

**orthogonal**projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix.We may describe, through all the points in an electric field which have the same potential, surfaces called equipotential surfaces, and these will be everywhere perpendicular or

**orthogonal**to the lines of electric force.In the case of non-intersecting circles, it is seen that the minimum circles of the coaxal system are a pair of points I and I', where the

**orthogonal**circle to the system intersects the line of centres; these points are named the " limiti,ng points."In the first place, each of these figures may be conceived as an

**orthogonal**projection of a closed plane-faced polyhedron.Work.The work done by a force acting on a particle, in any infinitely small displacement, is defined as the product of the force into the

**orthogonal**projection of the displacement on the direction of the force; i.e.AdvertisementThe area of the ellipse is 7rab, where a, b are the semi-axes; this result may be deduced by regarding the ellipse as the

**orthogonal**projection of a circle, or by means of the calculus.If the keyword FRACTIONAL is present, the translation is assumed to be in fractional coordinates, otherwise

**orthogonal**angstroms.Pass Point that lies on a local convexity that is

**orthogonal**to a local concavity.In all such cases, there is no component to plan convexity, any curvature being entirely

**orthogonal**to the xy plane.The only restriction is that the atomic coordinates are given in Angstroms on arbitrary

**orthogonal**axes.AdvertisementThis quantity is equal to the width of the error ellipse

**orthogonal**to the visibility vector.The wavelength associated with the vector resultant of these three

**orthogonal**propagation constants is just the free space wavelength lambda.They note " Computational modeling has strengths

**orthogonal**to the strengths of either traditional research discipline " (p. 7 ).The columns T are constrained to be mutually

**orthogonal**.The flags are not

**orthogonal**, in that more restrictive flags will often make less restrictive ones redundant.AdvertisementTalking about Perl's multimethod dispatch, he pointed out that multi is " now completely

**orthogonal**to scoping " .The rings have an O 120 o bridge, and are almost

**orthogonal**to each other.This strongly suggests that the philosophy of intelligent tutoring is really

**orthogonal**to the mindtool approach to learning.At the design stage, a design should be chosen to be as nearly

**orthogonal**as possible to the nuisance effects.Here,

**orthogonal**polynomials play an important role in the analysis.These estimators function on the principle that the noise subspace eigenvectors should be

**orthogonal**to the signal vectors.This theorem has been generalized for any tetrahedron; a sphere can be drawn through the four feet of the perpendiculars, and consequently through the mid-points of the lines from the vertices to the centre of the hyperboloid having these perpendiculars as generators, and through the

**orthogonal**projections of these points on the opposite faces.Note the equivalence of

**orthogonal**arrays with affine resolvable designs.Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces

**orthogonal**to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.The corresponding expression for two

**orthogonal**cylinders will be With a 2 = co, these reduce to / y /, = Uy (I ra 2 p22 +-C24)..The problem was to find the

**orthogonal**trajectories of a series of curves represented by a single equation.The inconvenience of

**orthogonal**illumination, which certainly gives better results, is avoided in the coaxial apparatus.