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  • ...tiplication]] operations can be [[simplify (mathematics)|simplified]] to a linear combination of distinct vectors. Linear combinations are for this reason often used as ...e space with the property that every vector can be uniquely expressed as a linear combination of the basis vectors. A [[linear transformation]] can be defined briefly a
    911 bytes (137 words) - 22:56, 25 November 2008
  • 177 bytes (27 words) - 09:33, 4 September 2009
  • 117 bytes (13 words) - 23:00, 25 November 2008

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  • ...tiplication]] operations can be [[simplify (mathematics)|simplified]] to a linear combination of distinct vectors. Linear combinations are for this reason often used as ...e space with the property that every vector can be uniquely expressed as a linear combination of the basis vectors. A [[linear transformation]] can be defined briefly a
    911 bytes (137 words) - 22:56, 25 November 2008
  • ...r free module, and such that no element of the set can be represented as a linear combination of the others.
    245 bytes (42 words) - 06:20, 4 September 2009
  • {{r|linear combination}}
    492 bytes (60 words) - 15:09, 28 July 2009
  • Functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method.
    141 bytes (18 words) - 04:48, 29 April 2009
  • ...y of a system of elements of a module or vector space, that no non-trivial linear combination is zero.
    149 bytes (23 words) - 16:48, 6 January 2009
  • ...[[module (algebra)|module]] or [[vector space]] is the set of all finite [[linear combination]]s of that set: it may equivalently be defined as the [[intersection]] of a
    968 bytes (162 words) - 13:20, 7 February 2009
  • ...that every element of <math>M</math> can be written uniquely as a finite [[linear combination]] of elements of <math>A</math>. The module <math>M</math> is said to be f ...such that every element of the module can be uniquely written as a finite linear combination of elements of the module. An equivalent definition of a basis for a modul
    2 KB (371 words) - 00:36, 2 February 2009
  • ...(mathematics)|ring]] or of a [[vector space]], is one for which the only [[linear combination]] equal to zero is that for which all the coefficients are zero (the "trivi
    2 KB (307 words) - 16:08, 7 February 2009
  • ...that every vector in <math>V</math> can be written uniquely as a finite [[linear combination]] of vectors in the basis. One may think of the vectors in a basis as buil
    3 KB (464 words) - 19:45, 1 December 2008
  • ...receding it, 1037, is the gcd. Now we want to write the gcd, 1037, as a [[linear combination]] of the two numbers we started with, in which the coefficients ''x'' and ' This gives 1037 as a linear combination of the two numbers in square brackets, which were among the successive rema
    7 KB (962 words) - 12:05, 3 May 2016
  • as an integer linear combination of the numbers (''a'',''b'') = ''ra'' + ''sb'' (with integers ''r'' and '' Since every such linear combination is divisible by all divisors common to
    5 KB (797 words) - 04:57, 21 April 2010
  • {{Image|Euclidean plane.png|right|350px|Fig. 1. Linear combination of vectors by the parallelogram rule. Construction is known as "parallelog ...cal-align: 20%"><math>\overrightarrow{OR}</math></font> resulting from the linear combination of <font style = "vertical-align: 20%"><math>\overrightarrow{OP}</math></f
    4 KB (632 words) - 10:13, 6 January 2010
  • ...ath>\mathbb{Z}/2\mathbb{Z}</math>, increasing all of the coefficients of a linear combination by <math>2</math> will result in the same element of the group.
    7 KB (1,154 words) - 02:39, 16 May 2009
  • ...enerated by a subset ''A'' may also be obtained as the set of all finite [[linear combination]]s of elements of ''A''.
    2 KB (414 words) - 03:00, 14 February 2010
  • ...<math>a</math>. The '''[[polynomial|polynomials]]''' then are [[finite]] [[linear combination|linear combinations]] of the monomials and the constant functions.
    8 KB (1,289 words) - 13:46, 26 May 2009
  • Every complex number is the real linear combination of the '''real unit'''
    3 KB (468 words) - 17:28, 1 January 2010
  • ...according to the Pauli principle. This problem can be overcome by taking a linear combination of two orbital products ...accurate theories (such as [[configuration interaction]] and [[MCSCF]]), a linear combination of Slater determinants is needed.
    11 KB (1,582 words) - 07:52, 23 September 2009
  • ...n function that is "smeared out" over a whole molecule. Usually an MO is a linear combination of [[atomic orbital]]s (an LCAO), which is a weighted sum of (almost) all a ...araday Soc., vol '''25''', p. 668 (1929).</ref> introduced the following ''linear combination of atomic orbitals'' (LCAO) way of writing an MO &phi;:
    8 KB (1,408 words) - 09:47, 24 April 2010
  • In addition, a linear combination of these solutions is also a solution:
    3 KB (459 words) - 07:58, 13 July 2012
  • By a simple linear combination of solid harmonics of &plusmn;''m'' these functions are transformed into re ====Linear combination ====
    16 KB (2,612 words) - 09:02, 9 February 2010

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