For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:

For them this was no time to cease firing, even as the survivors of the crew appeared on the outer casing, struggling out of their clothes to swim away from her.

For two years he worked quietly at Gray's Inn, until he was admitted as an outer barrister in 1582.

For Abelian groups all automorphisms except the trivial one are called outer automorphisms.

For example, the " jerk " produced by falling from outer space to the Earth is not particularly useful given the gravitational acceleration changes very slowly.

For example, a harder, more brittle steel may be sandwiched between an outer layer of softer, tougher, stainless steel to reduce vulnerability to corrosion.

For typical liver mitochondria, the area of the inner membrane is about five times as great as the outer membrane.

For example, the center segments return the ball a 90 ° angle in relation to the paddle, while the outer segments return the ball at smaller angles.

Heinlein's first novel, For Us, The Living ( written 1939 ), consists largely of speeches advocating the Social Credit system, and the early story " Misfit " ( 1939 ) deals with an organization that seems to be Franklin D. Roosevelt's Civilian Conservation Corps translated into outer space.

For most of its history, all of Rice's buildings have been contained within this " outer loop ".

For those that do not, extra insulation is often installed under the outer layer.

For example, during the June 19, 1986 overrun of the San Miguel Army base, FMLN sappers dressed only in black shorts, their faces blacked out with grease, sneaked through barbed wire at night, avoiding the searchlights, they made it to within firing range of the outer wall.

For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and then radiates into outer space.

For the 2012 season the Padres unveiled a new primary logo, featuring the cap logo inside a navy blue circle with the words " San Diego Padres Baseball Club " adorning the outer circle.

For example, the long-finned pilot whale secretes an enzymatic gel that rests on the outer surface of this animal and helps prevent other organisms from establishing colonies on the surface of these whales ' bodies.

For telecommunications-grade fibers, the reference surface is the outer surface of the cladding.

For coax of common impedance this mode is effectively suppressed but in high impedance coax and on a single central conductor without any outer shield, low attenuation and very broadband propagation is supported.

For example, if the lead of a screw is 1 mm, but the major diameter ( here, outer diameter ) is 10 mm, then the circumference of the screw is 10π, or about 31. 4 mm.

For either standard taper joints or ball-and-socket joints, inner and outer joints with the same numbers are made to fit together.

For this reason, if the outer surface of the apparatus were to consist of layers of a very infusible hard substance with layers of a poor heat conductor between, the surface would not be eroded to any considerable extent, especially as the velocity of the apparatus would not be nearly so great as that of the average meteor.

For let us suppose that the function F ( fx ) could be its own argument: in that case there would be a proposition ' F ( F ( fx ))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O ( f ( x )) and the outer one has the form Y ( O ( fx )).

For high-power radio-frequency transmission up to about 1 GHz, coaxial cable with a solid copper outer conductor is available in sizes of 0. 25 inch upward.

For the more general iteration, it has been proved that if the Julia set is connected ( that is, if c belongs to the ( usual ) Mandelbrot set ), then there exist a biholomorphic map between the outer Fatou domain and the outer of the unit circle such that.

For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects.

For these, asha was the course of everything observable, the motion of the planets and astral bodies, the progression of the seasons, the pattern of daily nomadic herdsman life, governed by regular metronomic events such as sunrise and sunset.

For centuries, many philosophers and scientists supposed that extrasolar planets existed, but there was no way of knowing how common they were or how similar they might be to the planets of the Solar System.

For instance, in the 55 Cancri system the first planet – 55 Cancri b – was discovered in 1996 ; two additional farther planets were simultaneously discovered in 2002 with the nearest to the star being named 55 Cancri c and the other 55 Cancri d ; a fourth planet was claimed ( its existence was later disputed ) in 2004 and named 55 Cancri e despite lying closer to the star than 55 Cancri b ; and the most recently discovered planet, in 2007, was named 55 Cancri f despite lying between 55 Cancri c and 55 Cancri d. As of April 2012 the highest letter in use is " j ", for the unconfirmed planet HD 10180 j ( HD 10180 h is the confirmed planet with the highest letter ).

For example, the planets that orbit the pulsar PSR 1257 are often referred to with capital rather than lowercase letters.

For astrodynamics reasons, cheap spacecraft travel to other planets is only practical within certain time windows.

For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods.

For example, the motion of planets around the sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime.

For example, the Astronomical Almanac uses TT for its tables of positions ( ephemerides ) of the Sun, Moon and planets as seen from the Earth.

For example, to test Newton's Law of Gravitation in our solar system, one needs information about the masses and positions of the Sun and all the planets.

For example, in 1933 H. G. Wells postulated in The Shape of Things to Come a Second World War in which Nazi Germany and Poland are evenly matched militarily, fighting an indecisive war over ten years ; and Poul Anderson's early 1950s Psychotechnic League depicted a world undergoing a devastating nuclear war in 1958, yet by the early 21st century managing not only to rebuild the ruins on Earth but also engage in extensive space colonization of the Moon and several planets.

For planets with atmospheres of any substance, however, there is an alternative: an autonomous flying robot, or " aerobot ".

For example, both Kepler's laws of the motion of the planets and Galileo's theories of motion worked out for terrestrial objects are reducible to Newtonian theories of mechanics, because all the explanatory power of the former are contained within the latter.

For typical terrestrial planets with a mass of 0. 5 – 1 Earth masses, such an impact typically results in a single moon containing 4 % of the host planet's mass.

* For planets and other rotating celestial bodies, the angle of the axis of rotation with respect to the normal to plane of the orbit is sometimes also called inclination or axial inclination, but to avoid ambiguity can be called axial tilt or obliquity.

For planets from specific fictional milieux, use the following lists and categories:

For superior planets the planet would typically move through in the night sky slower than the stars.

For the Moon, Ptolemy began with Hipparchus ' epicycle-on-deferent, then added a device that historians of astronomy refer to as a " crank mechanism ": He succeeded in creating models for the other planets, where Hipparchus had failed, by introducing a third device called the equant.

For example, the orbits of some repeating comets, and meteoroids leaving them, are in resonant orbits with Jupiter or one of the other large planets – so many revolutions of one will equal another number of revolutions of the other.

For scientific uses, a modern planetary ephemeris comprises software that generates positions of the planets and often of their satellites, or of asteroids or comets at virtually any time desired by the user.

For bodies with atmospheres, the landing occurs after atmospheric entry ( or less precisely for other planets, atmospheric reentry ) and the lander is first a re-entry vehicle.

For most planets, the Newtonian model's predictions are accurate ; for Mercury, it is slightly inaccurate and the model of general relativity must be used instead.

For example, orbital elements, especially osculating elements for minor planets, are routinely given with reference to two dates: first, relative to a recent epoch for all of the elements: but some of the data are dependent on a chosen coordinate system, and then it is usual to specify the coordinate system of a standard epoch which often is not the same as the epoch of the data.