Difference between revisions of "Matrices"
From GeoGebra Manual
(spelling now ok - see discussion) |
(added v4 - added FormulaText use to display matrices - needs link to ReducedRowEchelonForm page) |
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− | <noinclude>{{Manual Page}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude> | + | <noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude> |
{{objects|general}} | {{objects|general}} | ||
GeoGebra also supports matrices, which are represented as a list of lists that contain the rows of the matrix. | GeoGebra also supports matrices, which are represented as a list of lists that contain the rows of the matrix. | ||
{{Example|In GeoGebra, <nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki> represents a 3x3 matrix.}} | {{Example|In GeoGebra, <nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki> represents a 3x3 matrix.}} | ||
+ | |||
+ | In order to display nicely a matrix in the Graphic View, using LaTeX formatting, use [[FormulaText]] command. | ||
+ | {{Example|In the input bar type <code>FormulaText[<nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki>]</code> to display the matrix using LaTeX formatting.}} | ||
+ | |||
==Matrix Operations== | ==Matrix Operations== | ||
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* [[Transpose Command|Transpose]][Matrix]: Transposes the given matrix | * [[Transpose Command|Transpose]][Matrix]: Transposes the given matrix | ||
* [[ApplyMatrix Command|ApplyMatrix]][Matrix,Object]: Apply affine transform given by matrix on object. | * [[ApplyMatrix Command|ApplyMatrix]][Matrix,Object]: Apply affine transform given by matrix on object. | ||
+ | * ReducedRowEchelonForm : converts the matrix to a reduced row-echelon form | ||
+ | {{description}} | ||
__NOTOC__ | __NOTOC__ |
Revision as of 11:51, 22 February 2011
GeoGebra also supports matrices, which are represented as a list of lists that contain the rows of the matrix.
Example: In GeoGebra, {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} represents a 3x3 matrix.
In order to display nicely a matrix in the Graphic View, using LaTeX formatting, use FormulaText command.
Example: In the input bar type
FormulaText[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]
to display the matrix using LaTeX formatting.
Matrix Operations
Addition and subtraction examples
- Matrix1 + Matrix2: Adds the corresponding elements of two compatible matrices.
- Matrix1 – Matrix2: Subtracts the corresponding elements of two compatible matrices.
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, 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, 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, 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 : converts the matrix to a reduced row-echelon form
Description of command / feature needed. Please enter it instead of this template into Manual:Matrices. so that it's included also to the public namespace. For more details see Project:HowTo |
Comments
Note: See the official forum for a more detailed discussion about the multiplication of matrices.