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Every linear function on a finite-dimensional space is continuous.

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## Some Related Sentences

Every and linear

__Every__module over

**a**division ring has

**a**basis ;

__linear__maps between

**finite-dimensional**modules over

**a**division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable

**.**

__Every__time

**a**diode switches from

**on**to off or vice versa, the configuration of the

__linear__network changes

**.**

__Every__vector v in determines

**a**

__linear__map from R to taking 1 to v, which can be thought of as

**a**Lie algebra homomorphism

**.**

__Every__smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural

__linear__maps between the corresponding tangent spaces:

*

__Every____linear__combination of its components Y =**a**< sub > 1 </ sub > X < sub > 1 </ sub > + … +**a**< sub > k </ sub > X < sub > k </ sub >**is**normally distributed**.**__Every__

**continuous**

**function**in the

**function**

**space**can be represented as

**a**

__linear__combination of basis functions, just as every vector in

**a**vector

**space**can be represented as

**a**

__linear__combination of basis vectors

**.**

__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__physical quantity has

**a**Hermitian

__linear__operator associated to it, and the states where the value of this physical quantity

**is**definite are the eigenstates of this

__linear__operator

**.**

__Every__nontrivial proper rotation in 3 dimensions fixes

**a**unique 1-dimensional

__linear__subspace of R < sup > 3 </ sup > which

**is**called the axis of rotation ( this

**is**Euler's rotation theorem ).

__Every__

**finite-dimensional**normed

**space**

**is**reflexive, simply because in this case, the

**space**, its dual and bidual all have the same

__linear__dimension, hence the

__linear__injection J from the definition

**is**bijective, by the rank-nullity theorem

**.**

__Every__

**finite-dimensional**Hausdorff topological vector

**space**

**is**reflexive, because J

**is**bijective by

__linear__algebra, and because there

**is**

**a**unique Hausdorff vector

**space**topology

**on**

**a**finite dimensional vector

**space**

**.**

__Every__bounded

__linear__transformation from

**a**normed vector

**space**to

**a**complete, normed vector

**space**can be uniquely extended to

**a**bounded

__linear__transformation from the completion of to

**.**

__Every__vector

**a**in three dimensions

**is**

**a**

__linear__combination of the standard basis vectors i, j, and k

**.**

__Every__lattice in can be generated from

**a**basis for the vector

**space**by forming all

__linear__combinations with integer coefficients

**.**

__Every__

__linear__program has

**a**dual problem with the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa

**.**

Every and function

__Every__such subset has

**a**smallest element, so to specify our choice

__function__we can simply say that it maps each set to the least element of that set

**.**

__Every__contraction mapping

**is**Lipschitz

**continuous**and hence uniformly

**continuous**( for

**a**Lipschitz

**continuous**

__function__, the constant k

**is**no longer necessarily less than 1 ).

__Every__effectively calculable

__function__( effectively decidable predicate )

**is**general recursive italics

__Every__bijective

__function__g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

__Every__entire

__function__can be represented as

**a**power series that converges uniformly

**on**compact sets

**.**

__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__completely multiplicative

__function__

**is**

**a**homomorphism of monoids and

**is**completely determined by its restriction to the prime numbers

**.**

__Every__time another object or customer enters the line to wait, they join the end of the line and represent the “ enqueue ”

__function__

**.**

__Every__type that

**is**

**a**member of the type class defines

**a**

__function__that will extract the data from the string representation of the dumped data

**.**

__Every__output of an encoder can be described by its own transfer

__function__, which

**is**closely related to the generator polynomial

**.**

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