Transposition is a mathematical operation that involves changing the position of elements in a set or matrix. In linear algebra, for example, transposing a matrix means flipping it over its diagonal, turning rows into columns and vice versa. This operation is useful in various calculations, including solving systems of equations. In music, transposition refers to changing the key of a piece, which means shifting all the notes up or down by a consistent interval. This allows musicians to play the same piece in different keys, making it easier to perform with various instruments or vocal ranges.