For non-circular orbits or trajectories, only the component of gravitational force directed orthogonal to the path ( toward the center of the osculating circle ) is termed centripetal ; the remaining component acts to speed up or slow down the satellite in its orbit.

For quadratic forms of any signature, an orthogonal basis

For the real case this corresponds to the dot product of the results of directionally differential scaling of the two vectors, with positive scale factors and orthogonal directions of scaling.

For orthogonal idempotents a and b, is also idempotent, and we have and.

For example, the orthogonal group O < sub > n </ sub >( R ) consists of matrices A with AA < sup > T </ sup > = 1, so the Lie algebra consists of the matrices m with ( 1 + εm )( 1 + εm )< sup > T </ sup > = 1, which is equivalent to m + m < sup > T </ sup > = 0 because ε < sup > 2 </ sup > = 0.

For ideal positional accuracy, it is desirable to operate on a navigational grid where the grid lines are closer to right angles ( orthogonal ) to each other.

For this reason Ganda linguists use the orthogonal numbering system when discussing Ganda grammar ( other than in the context of Bantu comparative linguistics ), giving the 10 traditional noun classes of that language.

For propagation effects in two orthogonal modes, the Jones matrix can be written as

For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length ( usually denoted a ); similarly for the reciprocal lattice.

For example, it is often desirable to compute an orthonormal basis for a space, or an orthogonal change of bases ; both take the form of orthogonal matrices.

) For a near-orthogonal matrix, rapid convergence to the orthogonal factor can be achieved by a " Newton's method " approach due to ( 1990 ), repeatedly averaging the matrix with its inverse transpose.

More explicitly: For every symmetric real matrix A there exists a real orthogonal matrix Q such that D = Q < sup > T </ sup > AQ is a diagonal matrix.

For the special case of orthogonal isotropy, there are three different material property constants for each of Young's Modulus, Shear Modulus and Poisson's ratio — a total of 9 constants to describe the relationship between forces / moments and strains / curvatures.

For other non-singular forms O ( p, q ), see indefinite orthogonal group.

For an orthogonal matrix R, note that det R < sup > T </ sup >

For a stable method of converting an orthogonal matrix to a quaternion, see Rotation_matrix # Quaternion.

For a general inner product space V, an orthonormal basis can be used to define normalized orthogonal coordinates on V. Under these coordinates, the inner product becomes dot product of vectors.

For a system S, defined abstractly in such a way that it has N distinguishable states ( orthogonal quantum states ) that are consistent with its description, the amount of information I ( S ) contained in the system's state can be said to be log ( N ).

For constraint programming, Oz introduces the idea of " computation spaces "; these allow user-defined search and distribution strategies orthogonal to the constraint domain.

an almost complex structure as follows: For a tangent vector v we define J ( v ) as the vector of the same length which is orthogonal to v and such that ( v, J ( v )) is positively oriented.

For an example, take the special orthogonal groups in even dimension.

For complex spaces, all groups O ( p, q ; C ) are isomorphic to the usual orthogonal group O ( p + q ; C ), since the transform changes the signature of a form.

For the moment, suppose that the zeroth-order energy level is not degenerate, i. e. there is no eigenstate of in the orthogonal complement of with the energy.

For such a plane curve, there exists a reparametrization with respect to arc length s. This is a parametrization of C such that

For example, given the four points the pencil of conics through them can be parameterized as yielding the following pencil ; in all cases the center is at the origin :< ref group =" note "> A simpler parametrization is given by which are the affine combinations of the equations and corresponding the parallel vertical lines and horizontal lines, and results in the degenerate conics falling at the standard points of

For a given parametrized curve γ ( t ) the natural parametrization is unique up to shift of parameter.

For integrals of scalar fields, the answer to this question is simple, the value of the surface integral will be the same no matter what parametrization one uses.

For example, given the four points the pencil of conics through them can be parameterized as which are the affine combinations of the equations and corresponding to the parallel vertical lines and horizontal lines ; this yields degenerate conics at the standard points of A less elegant but more symmetric parametrization is given by in which case inverting a () interchanges x and y, yielding the following pencil ; in all cases the center is at the origin:

For each i, let Af.

For many Muslims, i ' thar must be practiced as a religious obligation during specific Islamic holidays.

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

For the incremental case ( i. e., ), this simplifies to:

For example, where a person has committed harmful actions of body, speech and mind based on greed, hatred and delusion, rebirth in a lower realm, i. e. an animal, a ghost or a hell realm, is to be expected.

For private suits only the victims or their families could prosecute, while for public suits anyone ( ho boulomenos, ' whoever wants to ' i. e. any citizen with full citizen rights ) could bring a case since the issues in these major suits were regarded as affecting the community as a whole.

For example, the giant elliptical galaxy M87 has an absolute magnitude of − 22 ( i. e. as bright as about 60, 000 stars of magnitude − 10 ).

For example, an array of 10 integer variables, with indices 0 through 9, may be stored as 10 words at memory addresses 2000, 2004, 2008, … 2036, so that the element with index i has the address 2000 + 4 × i.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.

For example, an " anti-realist " who denies that other minds exist ( i. e., a solipsist ) is quite different from an " anti-realist " who claims that there is no fact of the matter as to whether or not there are unobservable other minds ( i. e., a logical behaviorist ).

For a rigid body rotating around an axis of symmetry ( e. g. the blades of a ceiling fan ), the angular momentum can be expressed as the product of the body's moment of inertia, I, ( i. e. a measure of an object's resistance to changes in its rotation rate ) and its angular velocity ω:

For instance, chapter 6 ( B '), which ought to follow chapter 7 ( A ') chronologically, is put in parallel with chapter 3 ( B ) because they both deal with the persecution of Daniel and his friends i. e. " God's people.

For many years, apocryphal rumors circulated that a jealous lover had poisoned his coffee, but a more likely scenario is that he died of a bad heart attack after becoming disoriented during a snowstorm ( i. e., he froze to death ).

For objectivists, probability objectively measures the plausibility of propositions, i. e. the probability of a proposition corresponds to a reasonable belief everyone ( even a " robot ") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by requirements of rationality and consistency.

For example, most areas of law in most Anglo-American jurisdictions include " statutory law " enacted by a legislature, " regulatory law " promulgated by executive branch agencies pursuant to delegation of rule-making authority from the legislature, and common law or " case law ", i. e., decisions issued by courts ( or quasi-judicial tribunals within agencies ).

For example, a ( strict ) 2-category is a category together with " morphisms between morphisms ", i. e., processes which allow us to transform one morphism into another.

For example, if function div stands for the division operation x / y, then div with the parameter x fixed at 1 ( i. e., div 1 ) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv ( y )

For example, while in a conversion to Judaism a convert must accept basic Jewish principles of faith, and renounce all other religions, the process is more like a form of adoption, or changing national citizenship ( i. e. becoming a formal member of the people, or tribe ), with the convert becoming a " child of Abraham and Sarah.

For real values of, we have and for purely imaginary we have hence has a limit at 0 ( i. e., ƒ is complex differentiable at 0 ) if and only if.

For instance, low-end versions of complex architectures ( i. e. using less hardware ) could lead to situations where it was possible to improve performance by not using a complex instruction ( such as a procedure call or enter instruction ), but instead using a sequence of simpler instructions.