Question

What does the transpose transformation do?

Answer 1

The transpose transformation is a mathematical operation that switches the rows and columns of a matrix.

Step-by-step explanation:

The transpose transformation is a mathematical operation that switches the rows and columns of a matrix. It is denoted by the superscript 'T' and can be applied to both square and rectangular matrices. By taking the transpose of a matrix, the positions of its elements are swapped along the main diagonal.

1. For example, given the matrix A = [[1, 2], [3, 4]], the transpose of A is A^T = [[1, 3], [2, 4]].
2. The transpose transformation has several important properties, such as the fact that taking the transpose twice results in the original matrix: (A^T)^T = A.
3. The transpose operation is widely used in various areas of mathematics, including linear algebra, vector calculus, and statistics.