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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|general}} 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。 {{Example|1=在 GeoGebra 中,用 <nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki> 表示一個 3x3 矩陣 <math>\begin{pmatrix}1&2&3\\ 4&5&6\\ 7&8&9 \end{pmatrix}</math>}} 要在 [[File:Menu view graphics.svg|link=|16px]] '''[[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'''。 {{Example|1=在[[指令列]]輸入 <code>FormulaText[<nowiki>{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}</nowiki>]</code> 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: {{Example|1=假設矩陣 <code>matrix={{1, 2}, {3, 4}}</code>,則:<div> *<code>matrix(1, 1)</code> 取出第一列第一行的元素:''1''。 *<code>matrix(2, 2)</code>、<code>matrix(-1,2)</code>、<code>matrix(2,-1)</code> 和 <code>matrix(-1,-1)</code> 等指令都是取出第二列第二行的元素:''4''。 *一般來說,<code>matrix(''i'', ''j'')</code>( ''i'' 和 ''j'' 為整數)會取出矩陣第 ''i'' 列第 ''j'' 行的元素。</div>}} ==矩陣運算== Matrix operations are ''operations with lists'', so the following syntaxes produce the described results. {{Note|1=Some syntaxes can represent operations which are not defined in the same way in the matrices set.}} ===加法與減法=== * <code>Matrix1 + Matrix2</code>: adds the corresponding elements of two compatible matrices. * <code>Matrix1 – Matrix2</code>: subtracts the corresponding elements of two compatible matrices. ===乘法與除法=== * <code>Matrix * Number</code>: multiplies each element of ''Matrix'' by the given ''Number''. * <code>Matrix1 * Matrix2</code>: 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}} yields the matrix {{9, 12, 15}, {19, 26, 33}, {29, 40, 51}}.}} * <code>2x2 Matrix * Point (or Vector)</code>: multiplies the ''Matrix'' by the given ''Point / Vector'' and yields a point. : {{example|1={{1, 2}, {3, 4}} * (3, 4) yields the point ''A'' = (11, 25).}} * <code>3x3 Matrix * Point (or Vector)</code>: multiplies the ''Matrix'' by the given ''Point / Vector'' and yields a point. : {{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>.}} * <code>Matrix1 / Matrix2</code>: Divides each element of ''Matrix1'' by the corresponding element in ''Matrix2''. :{{note|1=However, GeoGebra supports the syntax <code><nowiki>Matrix1 * Matrix2 ^(-1)</nowiki></code> .}} ==其他運算== The section [[Matrix Commands]] contains the list of all available commands related to matrices, such as: * [[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__
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