矩陣

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GeoGebra 支援实数矩阵，将矩阵的每一列作为元素，以二维串列来储存矩阵。

范例： 在 GeoGebra 中，用 {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} 表示一个 3x3 矩阵 \begin{pmatrix}1&2&3\\ 4&5&6\\ 7&8&9 \end{pmatrix}

要在 绘图区用 LaTeX 格式显示一个矩阵，可以使用 FormulaText_指令，或从代数区拖曳一个矩阵物件放到绘图区。

范例： 在指令列输入 FormulaText[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] 会产生一个 LaTeX 格式的矩阵。

取用矩阵的元素

想要取用串列的特定元素（element），您可以使用 Element_指令或下列范例中的简化语法：

范例： 假设矩阵 matrix={{1, 2}, {3, 4}}，则：

• matrix(1, 1) 取出第一列第一行的元素：1。
• matrix(2, 2)、matrix(-1,2)、matrix(2,-1) 和 matrix(-1,-1) 等指令都是取出第二列第二行的元素：4。
• 一般来说，matrix(i, j)（ i 和 j 为整数）会取出矩阵第 i 列第 j 行的元素。

矩阵运算

Matrix operations are operations with lists, so the following syntaxes produce the described results.

备注： Some syntaxes can represent operations which are not defined in the same way in the matrices set.

加法与减法

• Matrix1 + Matrix2: adds the corresponding elements of two compatible matrices.
• Matrix1 – Matrix2: subtracts the corresponding elements of two compatible matrices.

乘法与除法

• Matrix * Number: multiplies each element of Matrix by the given Number.
• Matrix1 * Matrix2: uses matrix multiplication to calculate the resulting matrix.

备注： The rows of the first and columns of the second matrix need to have the same number of elements.

范例： {{1, 2}, {3, 4}, {5, 6}} * {{1, 2, 3}, {4, 5, 6}} yields the matrix {{9, 12, 15}, {19, 26, 33}, {29, 40, 51}}.

• 2x2 Matrix * Point (or Vector): multiplies the Matrix by the given Point / Vector and yields a point.

范例： {{1, 2}, {3, 4}} * (3, 4) yields the point A = (11, 25).

• 3x3 Matrix * Point (or Vector): multiplies the Matrix by the given Point / Vector and yields a point.

范例： {{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * (1, 2) gives you the point A = (8, 20).

备注： 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}.

• Matrix1 / Matrix2: Divides each element of Matrix1 by the corresponding element in Matrix2.

备注： However, GeoGebra supports the syntax Matrix1 * Matrix2 ^(-1) .

其他运算

The section Matrix Commands contains the list of all available commands related to matrices, such as:

• 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