Vector space - Revision history

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-20T14:43:33Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-17T18:14:17Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ ITA 6th edition

2017-04-11T16:58:39Z

‎See also: ITA 6th edition

MassimoNespolo: typos (missing or extra spaces in lang.)

2016-12-20T12:12:31Z

typos (missing or extra spaces in lang.)

MassimoNespolo: typo

2016-10-19T11:17:41Z

typo

MassimoNespolo: languages

2008-04-09T20:33:59Z

languages

BrianMcMahon at 13:18, 9 April 2008

2008-04-09T13:18:08Z

MassimoNespolo at 16:41, 27 February 2007

2007-02-27T16:41:17Z

New page

For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by |'''r'''| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.
The maximal number of linearly independent vectors in a vector space is called the ''dimension of the space''.

An essential difference between the behaviour of vectors and points is provided by the changes in their coefficients and coordinates if a different origin in point space is chosen. The coordinates of the points change when moving from an origin to the other one. However, the coefficients of the vector '''r''' do not change.

The [[point space]] is a dual of the vector space because to each vector in vector space a pair of points in [[point space]] can be associated.

Face normals, translation vectors, [[Patterson]] vectors and [[reciprocal lattice]] vectors are elements of vector space.
==See also==
* Chapter 8.1 in the ''International Tables for Crystallography Volume A''
* [http://www.iucr.org/iucr-top/comm/cteach/pamphlets/22/index.html Matrices, Mappings and Crystallographic Symmetry], teaching pamphlet No. 22 of the [[International Union of Crystallography]]

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 14:43, 20 November 2017
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−	<font color="blue">Espace vectoriel</font> (''Fr''). <~~Font~~ color="black">Spazio vettoriale</~~Font~~> (''It''). <~~Font~~ color="purple">ベクトル空間</~~Font~~> (''Ja'').	+	<font color="blue">Espace vectoriel</font> (''Fr''). <font color="red">Vektorraum</font> (''Ge''). <font color="black">Spazio vettoriale</font> (''It''). <font color="purple">ベクトル空間</font> (''Ja''). <font color="green">Espacio vectorial</font> (''Sp'').

@@ Line 1: / Line 1: @@
-<font color="blue">Espace vectoriel</font> (''Fr''); <Font color="black">Spazio vettoriale</Font> (''It''); <Font color="purple">ベクトル空間</Font> (''Ja'')
+<font color="blue">Espace vectoriel</font> (''Fr''). <Font color="black">Spazio vettoriale</Font> (''It''). <Font color="purple">ベクトル空間</Font> (''Ja'').
 For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by |'''r'''| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.
 The maximal number of linearly independent vectors in a vector space is called the ''dimension of the space''.
-An essential difference between the behaviour of vectors and points is provided by the changes in their coefficients and coordinates if a different origin in point space is chosen. The coordinates of the points change when moving from an origin to the other one. However, the coefficients of the vector '''r''' do not change.
+An essential difference between the behaviour of vectors and points is provided by the changes in their coefficients and coordinates if a different origin in point space is chosen. The coordinates of the points change when moving from one origin to another one. However, the coefficients of the vector '''r''' do not change.
 The [[point space]] is a dual of the vector space because to each vector in vector space a pair of points in [[point space]] can be associated.
@@ Line 11: / Line 12: @@
 ==See also==
-* Section 1.3.2 in the ''International Tables for Crystallography Volume A'', 6<sup>th</sup> edition
+* Chapter 1.3.2 of ''International Tables for Crystallography, Volume A'', 6th edition
-* [http://www.iucr.org/iucr-top/comm/cteach/pamphlets/22/index.html Matrices, Mappings and Crystallographic Symmetry], teaching pamphlet No. 22 of the [[International Union of Crystallography]]
+* [http://www.iucr.org/iucr-top/comm/cteach/pamphlets/22/index.html ''Matrices, Mappings and Crystallographic Symmetry''] (Teaching Pamphlet No. 22 of the International Union of Crystallography)
 [[Category:Fundamental crystallography]]

← Older revision		Revision as of 12:12, 20 December 2016
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−	<font color="blue">Espace vectoriel</font> (''Fr''); <Font color="black">Spazio vettoriale</Font>(''It'');　<Font color="purple"> ベクトル空間</Font>(''Ja'')	+	<font color="blue">Espace vectoriel</font> (''Fr''); <Font color="black">Spazio vettoriale</Font> (''It''); <Font color="purple">ベクトル空間</Font> (''Ja'')

	For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by \|'''r'''\| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.		For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by \|'''r'''\| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.

← Older revision		Revision as of 11:17, 19 October 2016
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−	<font color="blue">Espace vectoriel</font> (''Fr''); <Font color="black">Spazio vettoriale</Font>(''It'');　<Font color="purple"> ~~ベクタ空間~~</Font>(''Ja'')	+	<font color="blue">Espace vectoriel</font> (''Fr''); <Font color="black">Spazio vettoriale</Font>(''It'');　<Font color="purple"> ベクトル空間</Font>(''Ja'')

	For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by \|'''r'''\| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.		For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by \|'''r'''\| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.

← Older revision		Revision as of 20:33, 9 April 2008
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		+	<font color="blue">Espace vectoriel</font> (''Fr''); <Font color="black">Spazio vettoriale</Font>(''It'');　<Font color="purple"> ベクタ空間</Font>(''Ja'')
		+
	For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by \|'''r'''\| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.		For each pair of points X and Y in [[point space]] one can draw a vector '''r''' from X to Y. The set of all vectors forms a '''vector space'''. The vector space has no origin but instead there is the ''zero vector'' which is obtained by connecting any point X with itself. The vector '''r''' has a ''length'' which is designed by \|'''r'''\| = r, where r is a non–negative real number. This number is also called the ''absolute value'' of the vector.
	The maximal number of linearly independent vectors in a vector space is called the ''dimension of the space''.		The maximal number of linearly independent vectors in a vector space is called the ''dimension of the space''.