Page "Duality (mathematics)" ¶ 22
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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 octonion is a real linear combination of the unit octonions:
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 vector in the space may be written as a linear combination of unit vectors.
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 real m-by-n matrix yields a linear map from R < sup > n </ sup > to R < sup > m </ sup >.
* Every ( biregular ) algebraic automorphism of a projective space is projective linear.
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 irreducible polynomial in K which has a root in L factors into linear factors in L.
Every linear function on a finite-dimensional space is continuous.

Every and program
Every computer system provides at least one file-manager program for its native file system.
Every access to the translated file, or files below a hierarchy in the second case, is in fact handled by the program.
Every library module has at least two source files: a definitions file specifying the library's interface plus one or more program files specifying the implementation of the procedures in the interface.
Every executable program is made up of a series of these atomic instructions.
: Every program attempts to expand until it can read mail.
: Every program in development at MIT expands until it can read mail.
Bryan's words gave rise to later economic and political philosophies, including Huey Long's 1930s Share Our Wealth program, with its trigger phrase, " Every Man a King " inspired by Bryan's speech.
Every software keylogger can log these typed characters sent from one program to another.
Every student of the engineering trainee program receives the degree of “ ingénieur de l ' École centrale de Nantes ”, more commonly called “ ingénieur centralien ”.
Every member of the Bene Gesserit is conditioned into singular loyalty to the order and its goals with allegiances to even family being secondary, and no goal is more paramount than the Sisterhood's large-scale breeding program.
Long created the Share Our Wealth program in 1934 with the motto " Every Man a King ", proposing new wealth redistribution measures in the form of a net asset tax on corporations and individuals to curb the poverty and homelessness endemic nationwide during the Great Depression.
Every Christmas Singsaas puts out a CD of their annual Christmas program.
Every school within the Institute does require that applicants send in an artist's statement, along with a portfolio or audition ( depending on the program ) in order to be considered for admission.
Every program involving either Catholic or Protestant churches in which we participated was carefully scrutinized .... Every topic which had possible theological nuances or implications was vetoed, and only when the Rav pronounced it to be satisfactory did we proceed to the dialogue.
B ' nai B ' rith also publishes program guides for local Jewish education programs and each year sponsors " Unto Every Person There is a Name ".
Every action that influences an organization's improvement program in a change agent-client system relationship can be said to be an intervention.
Every year, the Ohio program holds a bill rating on a Saturday morning at the state house in Columbus.
Every line of a Microsoft BASIC program was assigned a line number by the programmer.
Every team in the league except the Detroit Red Wings and the New Jersey Devils have introduced a third jersey at one point since the program began.
Every evening from this time on Gribelin brought to him at the Military Club the program for the next day ; Du Paty and Henry, whose connection with the affair Esterhazy soon knew, saw him several times, sometimes at the Montmartre cemetery, sometimes on the Pont d ' Alexandre III.
Save the Children is working to achieve this goal through their Every One Campaign and their seven step program stating:
Every year, the annual Christmas in Washington program is filmed at the museum, with the President and First Lady.
Every Sunday, Polish Radio Katowice broadcasts a program based on famous prewar Lwów's Merry Wave, every Tuesday, Polish Radio Rzeszów broadcasts a program Kresy Landscapes.

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