transpose

• 指将矩阵的行与列互换得到的新矩阵，即转置矩阵。也指这种互换行列的操作或变换。

A noun referring to a matrix formed by interchanging the rows and columns of a given matrix.

1. Matrix transposeC1formaltechnical

   A matrix formed by interchanging the rows and columns of a given matrix.

   转置矩阵

   • The transpose of matrix A is denoted as A^T.
   • To find the transpose, swap the rows and columns of the original matrix.
   • The transpose operation is fundamental in linear algebra.

• 动词，指改变事物的顺序、位置或排列，或将某物移到另一个地方或语境中。

A verb used to indicate the act of changing the order, position, or arrangement of something, or transferring something to a different place or context.

1. Change order or arrangementB2formal

   To alter the sequence or arrangement of items, often by swapping their positions.

   调换

   • The editor transposed two paragraphs in the article.
   • In the code, the programmer accidentally transposed the numbers.
   • When copying the list, she transposed the names of the two authors.

   同义词exchangeinterchangepermutereorderreverseswapswitch

2. Transfer from one place or period to anotherC1formal

   To move something from one location or time to another.

   转移

   • The novel transposes the story to a modern setting.
   • The artist transposed the scene from a photograph onto canvas.
   • The play transposes the events of the 19th century into a contemporary context.

   同义词carryconveymoverelocateshifttransfertransplanttransport

3. Cause to change placesB2formal

   To cause two or more things to exchange positions.

   调换位置

   • The magician transposed the two cards in his hand.
   • In the puzzle, you need to transpose the tiles to form the correct image.
   • The experiment transposed the roles of the two variables.

   同义词exchangeinterchangeswapswitch

4. Transfer a quantity in an equationC1formal

   In mathematics, to move a term from one side of an equation to the other, changing its sign to maintain equality.

   移项

   • To solve for x, transpose the constant term to the other side of the equation.
   • The student learned how to transpose terms in algebraic equations.
   • When you transpose the variable, remember to reverse its sign.

   同义词carry overmoveshifttransfer

5. Put music into another keyB2formal

   To rewrite or perform a piece of music in a different key.

   移调

   • The pianist transposed the song into a higher key for the singer.
   • The composer transposed the entire symphony for a smaller ensemble.
   • She transposed the melody from C major to G major.

6. Exchange positions without a change in valueC1formal

   To swap the positions of two elements while their values remain unchanged.

   转置

   • In the matrix, you can transpose rows and columns.
   • The algorithm transposes the data points to analyze the correlation.
   • When you transpose the coordinates, the distance remains the same.

   同义词exchangeinterchangepermuteswapswitch

7. Change keyB2formal

   To alter the key of a musical composition.

   移调

   • The guitarist transposed the song to a different key to match the vocal range.
   • The choir director transposed the hymn for the sopranos.
   • He transposed the piece from a minor key to a major key.