kids encyclopedia robot

Transpose facts for kids

Kids Encyclopedia Facts
This page is about the transpose of a matrix. For other uses, see Transposition (disambiguation).

The transpose of a matrix A is another matrix where the rows of A are written as columns. Vectors can be transposed in the same way. We can write the transpose of A using different symbols such as AT , A′ , Atr and At.

Examples

Here is the vector \begin{bmatrix} 1 & 2 \end{bmatrix} being transposed:

  • \begin{bmatrix} 1 & 2 \end{bmatrix}^{\mathrm{T}} \!\! \;\! = \, \begin{bmatrix} 1 \\ 2 \end{bmatrix}.

Here are a few matrices being transposed:

  • \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^{\mathrm{T}} \!\! \;\! = \, \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}.
  • \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}^{\mathrm{T}} \!\! \;\! = \, \begin{bmatrix} 1 & 3 & 5\\ 2 & 4 & 6 \end{bmatrix}. \;
  • \begin{bmatrix} 1 & 2 & 8 \\ 3 & 4 & 3 \\ 5 & 6 & 1 \end{bmatrix}^{\mathrm{T}} \!\! \;\! = \, \begin{bmatrix} 1 & 3 & 5\\ 2 & 4 & 6\\ 8 & 3 & 1 \end{bmatrix}. \;

Properties

Given two matrices A and B, the following properties related to the transpose are true:

  • (A^T)^{-1} = (A^{-1})^T
  • (AB)^T = B^T A^T

Related pages

Images for kids

  • Matrix transpose

    The transpose AT of a matrix A can be obtained by reflecting the elements along its main diagonal. Repeating the process on the transposed matrix returns the elements to their original position.

See also

Kids robot.svg In Spanish: Matriz transpuesta para niños

kids search engine
All content from Kiddle encyclopedia articles (including the article images and facts) can be freely used under Attribution-ShareAlike license, unless stated otherwise. Cite this article:
Transpose Facts for Kids. Kiddle Encyclopedia.