Transpose

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The transpose of a matrix A is what you get when you rewrite the matrix with its rows as columns. Vectors can be transposed in the same way.

We can write the transpose of A using different symbols:

  • AT
  • A
  • Atr
  • At

Examples[change | edit source]

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}. \;