矩陣

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GeoGebra 支援實數矩陣，將矩陣的每一列作為元素，以二維串列來儲存矩陣。

範例： 在 GeoGebra 中，用 {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} 表示一個 3x3 矩陣 \begin{pmatrix}1&2&3\\ 4&5&6\\ 7&8&9 \end{pmatrix}

要在 繪圖區用 LaTeX 格式顯示一個矩陣，可以使用 FormulaText_指令，或從代數區拖曳一個矩陣物件放到繪圖區。

範例： 在指令列輸入 FormulaText[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] 會產生一個 LaTeX 格式的矩陣。

取用矩陣的元素

想要取用串列的特定元素（element），您可以使用 Element_指令或下列範例中的簡化語法：

範例： 假設矩陣 matrix={{1, 2}, {3, 4}}，則：

• 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。
• 一般來說，matrix(i, j)（ i 和 j 為整數）會取出矩陣第 i 列第 j 行的元素。

矩陣運算

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

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

加法與減法

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

乘法與除法

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

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

範例： {{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.

範例： {{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.

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

備註： 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.

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

其他運算

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