Différences entre versions de « Matrices »
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<noinclude>{{Manual Page|version=4.0}}</noinclude>{{objects|general}} | <noinclude>{{Manual Page|version=4.0}}</noinclude>{{objects|general}} | ||
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| + | GeoGebra supporte aussi les matrices, qui sont représentées par une liste de listes contenant les lignes de la matrice. | ||
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| + | {{Example|1=Dans GeoGebra, <nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki> représente la matrice 3 <math> \times</math> 3 .}} | ||
| + | |||
| + | Afin d'afficher correctement une matrice dans Graphique, utilisez le format LaTeX à l'aide de la commande [[LaTeX]] . | ||
| + | {{Example|1=In the input bar type <code>LateX[<nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki>]</code> .}} | ||
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| + | ==Opérations sur les matrices== | ||
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| + | ===Addition et soustraction :=== | ||
| + | |||
| + | * Matrice1 + Matrice2 : Additionne les éléments correspondants des deux matrices compatibles. | ||
| + | * Matrice1 – Matrice2 : Soustrait les éléments correspondants des deux matrices compatibles. | ||
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| + | ===Multiplication examples=== | ||
| + | * Matrix * Number: Multiplies every element of the matrix by the given number. | ||
| + | * Matrix1 * Matrix2: Uses matrix multiplication to calculate the resulting matrix. | ||
| + | {{note|The rows of the first and columns of the second matrix need to have the same number of elements.}} | ||
| + | {{example|1={{1, 2}, {3, 4}, {5, 6}} * {{1, 2, 3}, {4, 5, 6}} gives you the matrix {{9, 12, 15}, {19, 26, 33}, {29, 40, 51}}.}} | ||
| + | * 2x2 Matrix * Point (or Vector): Multiplies the matrix with the given point/vector and gives you a point as a result. | ||
| + | {{example|1={{1, 2}, {3, 4}} * (3, 4) gives you the point A = (11, 25).}} | ||
| + | * 3x3 Matrix * Point (or Vector): Multiplies the matrix with the given point/vector and gives you a point as a result. | ||
| + | {{example|1={{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * (1, 2) gives you the point A = (8, 20).}} | ||
| + | {{note|1=This is a special case for affine transformations where homogeneous coordinates are used: (x, y, 1) for a point and (x, y, 0) for a vector. This example is therefore equivalent to: | ||
| + | <code><nowiki>{{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * {1, 2, 1}</nowiki></code>.}} | ||
| + | |||
| + | ==Other examples== | ||
| + | see also section [[Matrix Commands]] | ||
| + | |||
| + | * [[Determinant Command|Determinant]][Matrix]: Calculates the determinant for the given matrix. | ||
| + | * [[Invert Command|Invert]][Matrix]: Inverts the given matrix | ||
| + | * [[Transpose Command|Transpose]][Matrix]: Transposes the given matrix | ||
| + | * [[ApplyMatrix Command|ApplyMatrix]][Matrix,Object]: Apply affine transform given by matrix on object. | ||
| + | * [[ReducedRowEchelonForm Command|ReducedRowEchelonForm]][Matrix]: Converts the matrix to a reduced row-echelon form | ||
| + | |||
| + | __NOTOC__ | ||
Version du 20 juillet 2011 à 17:57
GeoGebra supporte aussi les matrices, qui sont représentées par une liste de listes contenant les lignes de la matrice.
Exemple: Dans GeoGebra, {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} représente la matrice 3 \times 3 .
Afin d'afficher correctement une matrice dans Graphique, utilisez le format LaTeX à l'aide de la commande LaTeX .
Exemple: In the input bar type
LateX[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] .
Opérations sur les matrices
Addition et soustraction :
- Matrice1 + Matrice2 : Additionne les éléments correspondants des deux matrices compatibles.
- Matrice1 – Matrice2 : Soustrait les éléments correspondants des deux matrices compatibles.
Multiplication examples
- Matrix * Number: Multiplies every element of the matrix by the given number.
- Matrix1 * Matrix2: Uses matrix multiplication to calculate the resulting matrix.
Note : The rows of the first and columns of the second matrix need to have the same number of elements.
Exemple: {{1, 2}, {3, 4}, {5, 6}} * {{1, 2, 3}, {4, 5, 6}} gives you the matrix {{9, 12, 15}, {19, 26, 33}, {29, 40, 51}}.
- 2x2 Matrix * Point (or Vector): Multiplies the matrix with the given point/vector and gives you a point as a result.
Exemple: {{1, 2}, {3, 4}} * (3, 4) gives you the point A = (11, 25).
- 3x3 Matrix * Point (or Vector): Multiplies the matrix with the given point/vector and gives you a point as a result.
Exemple: {{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * (1, 2) gives you the point A = (8, 20).
Note : This is a special case for affine transformations where homogeneous coordinates are used: (x, y, 1) for a point and (x, y, 0) for a vector. This example is therefore equivalent to:
{{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * {1, 2, 1}.Other examples
see also section Matrix Commands
- Determinant[Matrix]: Calculates the determinant for the given matrix.
- Invert[Matrix]: Inverts the given matrix
- Transpose[Matrix]: Transposes the given matrix
- ApplyMatrix[Matrix,Object]: Apply affine transform given by matrix on object.
- ReducedRowEchelonForm[Matrix]: Converts the matrix to a reduced row-echelon form
