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 the outer planets, each planet is predicted to be roughly twice as far from the Sun as the previous object.

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 a few details of the system the lines are 1-1/4'' '' X-Tru-Coat, a product of Republic Steel Corp., and all lines are welded.

For specialized types of displays, such as large three-dimensional units reproducing a product, package, human or animal figures, etc., reinforced plastics and rotationally molded vinyl plastisols are other materials frequently used.

For the purposes of setting the product price, the industry behaves as a single entity.

For reception, a local oscillator will typically restore the suppressed carrier so the signal can be demodulated with a product detector.

For example, in copper refining, copper anodes, an intermediate product from the furnaces, are electrolysed in an appropriate solution ( such as sulfuric acid ) to yield high purity ( 99. 99 %) cathodes.

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 an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:

For a rigorous treatment of the Dirac inner product of non-normalizable states see the definition given by D. Carfì in and.

For isotopes lighter than 112 u, the primary decay mode is electron capture and the dominant decay product is element 47 ( silver ).

For example, the quotient rule is a consequence of the chain rule and the product rule.

For example, feedback from a technical support center can enlighten marketers about specific services and product features clients are asking for.

For example, a sales transaction can be broken up into facts such as the number of products ordered and the price paid for the products, and into dimensions such as order date, customer name, product number, order ship-to and bill-to locations, and salesperson responsible for receiving the order.

For any n, the divergence is a linear operator, and it satisfies the " product rule "

For example, sales data might be aggregated to weekly totals and converted from internal product codes to use UPCs so that it can be compared with ACNielsen data.

For example, a rectangle with a width of 3 and a length of 4 has an area that represents the product, 12.

For example, some new product development projects place a high premium on finishing quickly.

The GCD of two numbers a and b is the product of the prime factors shared by the two numbers, where a same prime factor can be used multiple times, but only as long as the product of these factors divides both a and b. For example, since 1386 can be factored into 2 × 3 × 3 × 7 × 11, and 3213 can be factored into 3 × 3 × 3 × 7 × 17, the greatest common divisor of 1386 and 3213 equals 63 = 3 × 3 × 7, the product of their shared prime factors.

For example, on a set of quaternary ( i. e., 4-ary ) variables, representing the full function requires storing values, the value of the function for each element in the Cartesian product, i. e., each of the 1024 possible combinations for.

For example, a product package might include a logo or other artwork, organized text and pure design elements such as shapes and color which unify the piece.

For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product ; that is.

For example, all Jockey Club Thoroughbred registries require that a registered Thoroughbred be a product of a natural mating, so called " live cover ".