Difference between revisions of "Matrices"
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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. | ||
Revision as of 19:39, 19 December 2010
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 the matrix.
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 homogenous 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 trransform given by matrix on object.
Comments
Note: See the official forum for a more detailed discussion about the multiplication of matrices.