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334fe967
Commit
334fe967
authored
Aug 13, 2020
by
Claude Meny
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Update textbook.fr.md
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334fe967
...
...
@@ -170,23 +170,25 @@ de cet espace $`\mathcal{E}`$ se décompose de *façon unique* en une *combinais
$
`\vec{a_1},\vec{a_2},...,\vec{a_n}`
$.
<br>
[
EN
]
$
`n`
$ vectors ordered in a
*sequence $`(\vec{a_1},\vec{a_2},...,\vec{a_n})`$*
form a basis
of a vector space $
`\mathcal{E}`
$ of dimension $
`n`
$ if any vector of this space decomposes in a unique
way into a linear combination of the vectors $
`\vec{a_1},\vec{a_2},...,\vec{a_n}`
$.
<br>
<br>
[
ES
]
Para cualquier base denotamos los vectores base $
`\vec{a_i}`
$.
way into a linear combination of the vectors $
`\vec{a_1},\vec{a_2},...,\vec{a_n}`
$.
*
"$
`(\vec{e_1},\vec{e_2},...,\vec{e_n})`
$ est une base de $
`\mathcal{E}`
$"$
`
\quad\Longrightarrow \quad\forall \overrightarrow{V}\in\mathcal{E}`
$$
`\quad\exists ! (\alpha_1,\alpha_1,...;\alpha_1)\in\mathbb{R}^n`
$$
`\quad
\overrightarrow{V}=\alpha_1\cdot\overrightarrow{e_1}+\alpha_2\cdot\overrightarrow{e_2}+...+\alpha_n\cdot\overrightarrow{e_n}`
$
*
[
ES
]
Para cualquier base denotamos los vectores base $
`\vec{a_i}`
$.
(ejemplo : vectores de la base convencionale (no ortonormales) de un cristal en física
del estado sólido/estructura de materiales) :
<br>
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-08
<br>
Reservamos la notación $
`\vec{e_i}`
$ para las bases ortonormales :
<br>
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-28.
<br>
[
FR
]
Pour un base quelconque nous notons les vecteurs de base $
`\vec{a_i}`
$.
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-28.
<br>
<br>
[
FR
]
Pour un base quelconque nous notons les vecteurs de base $
`\vec{a_i}`
$.
(exemple des vecteurs de base conventionnelle (non orthonormée) d'un cristal,
en physique du solide/structure des matériaux) :
<br>
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-08
<br>
Nous réservons la notation $
`\vec{e_i}`
$ pour les vecteurs d'une base orthonormée :
<br>
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-28.
<br>
[
EN
]
For any base we denote the base vectors $
`\vec{a_i}`
$.
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-28.
<br>
<br>
[
EN
]
For any base we denote the base vectors $
`\vec{a_i}`
$.
(example of the conventional base (not orthonormal) of a crystal, in solid state
physics/structure of materials) :
<br>
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-08
<br>
...
...
@@ -194,11 +196,6 @@ We reserve the notation $`\vec{e_i}`$ for vectors of an orthonormal base :<br>
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-28.
$
`(\vec{e_1},\vec{e_2},...,\vec{e_n})``$
* "$`
(
\v
ec{e_1},
\v
ec{e_2},...,
\v
ec{e_n})
`$ est une base de $`
\m
athcal{E}
`$"$`
\q
uad
\L
ongrightarrow
\q
uad
\f
orall
\o
verrightarrow{V}
\i
n
\m
athcal{E}
`$$`
\q
uad
\e
xists ! (
\a
lpha_1,
\a
lpha_1,...;
\a
lpha_1)
\i
n
\m
athbb{R}^n
`$$`
\q
uad
\o
verrightarrow{V}=
\a
lpha_1
\c
dot
\o
verrightarrow{e_1}+
\a
lpha_2
\c
dot
\o
verrightarrow{e_2}+...+
\a
lpha_n
\c
dot
\o
verrightarrow{e_n}
`$
#### Sistemas de coordenadas / Systèmes de coordonnées - Repère de l’espace /
...
...
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