Transpose matrix is a mathematical symbol that different authors have identified in different ways in their books. E.g.

```
\documentclass{article}
\begin{document}
$$ \mathbf{A}^T = \mathbf{A} $$
$$ \mathbf{A}^\mathrm{T} = -\mathbf{A} $$
$$ \mathbf{A}^\top = \overline{\mathbf{A}}$$
$$ \mathbf{A}^\mathsf{T} = -\overline{\mathbf{A}} $$
$$ \mathbf{A}^\mathsf{t},\; \mathbf{A}^\mathsf{tr} $$
\end{document}
```

**Output : **

This `\top`

command is in multiple packages. And the shape is different from the default command.

```
\documentclass{article}
\usepackage{MnSymbol}
\begin{document}
$$ \left[\mathbf{A}^\top\right]_{ij} = \left[\mathbf{A}\right]_{ji}$$
$$
\begin{bmatrix}
11 & 12\\
13 & 14\\
15 & 16
\end{bmatrix}^\top =
\begin{bmatrix}
11 & 13 & 15\\
12 & 14 & 16
\end{bmatrix}
$$
\end{document}
```

**Output : **

## Use \intercal command for transpose matrix in LaTeX

You see more than one method at the point above but amssymb’s `\intercal`

command is the best practice to represent the capital letter `T`

.

```
\documentclass{article}
\usepackage{amssymb}
\begin{document}
$$ (\mathbf{A}+\mathbf{B})^\intercal = \mathbf{A}^\intercal + \mathbf{B}^\intercal $$
$$ (\mathbf{AB})^\intercal = \mathbf{B}^\intercal\mathbf{A}^\intercal $$
$$ (c\mathbf{A})^\intercal = c\mathbf{A}^\intercal $$
\end{document}
```

**Output : **

## Power of transpose matrix

Symbols have been defined in different ways in different books to use power on transpose matrix. In many cases, you will see that the superscripted `T`

has been used before the matrix, and then the power has been used.

```
\documentclass{article}
\begin{document}
$$ {^\mathsf{T}}\mathbf{A}^n,\;{^\mathsf{T}}\mathbf{A}^{-1} $$
$$ \left(\mathbf{A}^\mathsf{T}\right)^{-1} = \left(\mathbf{A}^{-1}\right)^\mathsf{T} $$
$$ \left( \mathbf{AA}^\mathsf{T} \right)^\mathsf{T} = \left( \mathbf{A}^\mathsf{T}\right)^\mathsf{T}\mathbf{A}^\mathsf{T} $$
\end{document}
```

**Output : **