Как транспонировать матрицу в wolfram mathematica

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Математика с WolframAlpha ® . Объяснения с примерами.

Транспонированная матрица

Матрица, полученная из данной матрицы заменой каждой ее строки на столбец с тем же номером, называется транспонированной к данной.

В Wolfram|Alpha для получения транспонированной матрицы служит запрос transpose.

Если вместо буквенных обозначений использовать числа, то Wolfram|Alpha, по запросу transpose кроме транспонированной матрицы выдает еще и другую сопутствующую информацию.

Wolfram|Alpha по запросу transpose выдает транспонированную матрицу для матрицы любого размера:

Транспонированная матрица имеет следующее свойство: transpose (transpose A) = A.

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Transpose

transposes list so that the k ^(th)level in list is the n k ^(th)level in the result.

transposes levels m and n in list , leaving all other levels unchanged.

Details and Options

    Transpose [ m ] gives the usual transpose of a matrix m . Transpose [ m ] can be input as m &#62407; . &#62407; can be entered as tr or \[Transpose] . For a matrix m , Transpose [ m ] is equivalent to Transpose [ m , < 2 , 1 >] . For an array a of depth r &#8805; 3 , Transpose [ a ] is equivalent to Transpose [ a , < 2 , 1 , 3 , &#8230; , r >] , only transposing the first two levels. The n i in Transpose [ a , < n 1 , n 2 , &#8230; > ] or Transpose [ a , n 1 &#61728; n 2 ] must be positive integers no larger than ArrayDepth [ a ] . If < n 1 , n 2 , &#8230; > is a permutation list, then the element at position < i 1 , i 2 , &#8230; > of Transpose [ a , < n 1 , n 2 , &#8230; > ] is the element at position < i n 1 , i n 2 , &#8230; > of the array a . For a permutation perm , the dimensions of Transpose [ a , perm ] are Permute [ Dimensions [ a ] , perm ] . A permutation list perm in Transpose [ a , perm ] can also be given in Cycles form, as returned by PermutationCycles [ perm ] . Transpose [ a , m &#8596; n ] or Transpose [ a , TwoWayRule [ m , n ] ] is equivalent to Transpose [ a , Cycles [ < < m , n >> ] ] . Transpose allows the n i to be repeated, computing diagonals of the subarrays determined by the repeated levels. The result is therefore an array of smaller depth. For a square matrix m , Transpose [ m , < 1 , 1 >] returns the main diagonal of m , as given by Diagonal [ m ] . In general, if n p = n q then the operation Transpose [ a , < n 1 , n 2 , &#8230; > ] is possible for an array a of dimensions < d 1 , d 2 , &#8230; > if d p = d q . Transpose works on SparseArray and structured array objects.

Examples

Basic Examples &#160; &#160; (2)

Transpose a 2 &#215; 3 matrix:

Use followed by tr to enter the transposition operator:

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