To change the order or position of something, especially letters, words, or musical notes. The composer decided to transpose the melody to a different key.
To transfer a mathematical term from one side of an equation to the other, changing its sign. To solve the equation, you need to transpose the variable to the other side.
To rewrite a piece of music in a different key. The choir director asked the pianist to transpose the song to a lower key for the performance.
(mathematics) To obtain the transpose of (a matrix) by interchanging its rows and columns. If the matrix is symmetric, transposing it will leave it unchanged.