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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.
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For and example
For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.
For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.
For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.
For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;
For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:
For example: 1.
For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.
For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.
For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.
For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;
For example, a 12-to-one engine would power a supersonic VTOL fighter.
For example: Af.
For example: Af.
For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.
For example: Af.
For example, let's consider a standard 283 cubic inch Chevy Aj.
For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.
For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.
For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.
For example, the Friday after Thanksgiving can be substituted for Washington's birthday.
For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.
For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.
For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.
For and orthogonal
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 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.
* For an orthogonal parametrization ( i. e., ), Gaussian curvature is:
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.
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