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Every real m-by-n matrix yields a linear map from R < sup > n </ sup > to R < sup > m </ sup >.

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## Some Related Sentences

Every and real

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__Every____real__Banach algebra which is**a**division algebra is isomorphic**to**the reals, the complexes, or the quaternions.
*

__Every__unital__real__Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic**to**the reals, the complexes, or the quaternions.
*

__Every__commutative__real__unital Noetherian Banach algebra with no zero divisors is isomorphic**to**the__real__or complex numbers.
*

__Every__commutative__real__unital Noetherian Banach algebra ( possibly having zero divisors ) is finite-dimensional.__Every__sequence that ran off

**to**infinity in the

__real__line will then converge

**to**∞ in this compactification.

__Every__holomorphic function can be separated into its

__real__and imaginary parts, and each of these is

**a**solution of Laplace's equation on

**R**

**<**

**sup**

**>**2

**</**

**sup**

**>.**

__Every__ordered field is

**a**formally

__real__field, i. e., 0 cannot be written as

**a**sum of nonzero squares.

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__Every__separable metric space is isometric**to****a**subset of the ( non-separable ) Banach space l**<****sup**>∞</**sup****>**of all bounded__real__sequences with the supremum norm ; this is known as the Fréchet embedding.__Every__non-negative

__real__number

**a**has

**a**unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix.

__Every__nonzero

__real__number has

**a**multiplicative inverse ( i. e. an inverse with respect

**to**multiplication ) given by ( or ).

__Every__sedenion is

**a**

__real__

**linear**combination of the unit sedenions 1,

**<**var

**>**e

**</**var >< sub

**>**1

**</**sub >,

**<**var

**>**e

**</**var >< sub

**>**2

**</**sub >,

**<**var

**>**e

**</**var >< sub

**>**3

**</**sub >, ..., and

**<**var

**>**e

**</**var >< sub

**>**15

**</**sub >,

__Every__Riemann surface is

**a**two-dimensional

__real__analytic manifold ( i. e.,

**a**surface ), but it contains more structure ( specifically

**a**complex structure ) which is needed for the unambiguous definition of holomorphic functions.

In his book Nirvana: The Stories Behind

__Every__Song, Chuck Crisafulli writes that the song " stands out in the Cobain canon as**a**song with**a**very specific genesis and**a**very__real__subject ".__Every__finite or bounded interval of the

__real__numbers that contains an infinite number of points must have at least one point of accumulation.

Every and matrix

__Every__aspect of the line

__matrix__printer is designed

**to**deliver higher reliability, fast throughput, and greater resistance

**to**rough handling and hazardous environmental conditions.

__Every__constraint is in turn

**a**pair ( usually represented as

**a**

__matrix__), where is an-tuple of variables and is an-ary relation on.

*

__Every__finite-dimensional simple algebra over**R**must be**a**__matrix__ring over**R**, C, or H.__Every__central simple algebra over**R**must be**a**__matrix__ring over**R**or H. These results follow**from**the Frobenius theorem.
*

__Every__finite-dimensional simple algebra over C must be**a**__matrix__ring over C and hence every central simple algebra over C must be**a**__matrix__ring over C.
*

__Every__finite-dimensional central simple algebra over**a**finite field must be**a**__matrix__ring over that field.
We call

**a**field E**a**splitting field for A if A ⊗ E is isomorphic**to****a**__matrix__ring over E.__Every__finite dimensional CSA has**a**splitting field: indeed, in the case when A is**a**division algebra, then**a**maximal subfield of A is**a**splitting field.
*

__Every__4-dimensional central simple algebra over**a**field F is isomorphic**to****a**quaternion algebra ; in fact, it is either**a**two-by-two__matrix__algebra, or**a**division algebra.__Every__object in the drawing can be subjected

**to**arbitrary affine transformations: moving, rotating, scaling, skewing and

**a**configurable

__matrix__.

__Every__pixel

**from**the secret image is encoded into multiple subpixels in each share image using

**a**

__matrix__

**to**determine the color of the pixels.

Every and yields

__Every__non-inner automorphism

__yields__

**a**non-trivial element of Out ( G ), but different non-inner automorphisms may yield the same element of Out ( G ).

__Every__gap sequence that contains 1

__yields__

**a**correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

*

__Every__cover is**a**local homeomorphism — that is, for every, there exists**a**neighborhood of c and**a**neighborhood of such that the restriction of p**to**U__yields__**a**homeomorphism**from**U**to**V. This implies that C and X share all local properties.__Every__year the Salesianum vs. St Mark's football game

__yields__one of the largest turnouts in Delaware and the game is labeled " The Holy War "

0.338 seconds.