**Command Summary**

This command calculates the transpose of a matrix.

**Command Syntax**

*matrix*^{T}

**Menu Location**

Press:

- MATRX (on the 83) or 2nd MATRX (83+ or higher) to access the Matrix menu.
- LEFT to access the MATH submenu
- 2 to select
^{T}, or use arrows

**Calculator Compatibility**

TI-83/84/+/SE

**Token Size**

The ^{T} command is used to calculate the transpose of a matrix: it flips a matrix along its main diagonal. This means that the (i,j)th element becomes the (j,i)th element, and vice versa. As a result, the transpose of an M by N matrix is an N by M matrix.

[[1,2,3][4,5,6]]

………… [[1 2 3]

…………. [4 5 6]]

Ans^{T}

………… [[1 4]

…………. [2 5]

…………. [3 6]]

# Advanced Uses

In addition to its many uses in linear algebra, the ^{T} operation is useful to programmers: with operations such as Matr►list( and augment(, which normally deal with columns, ^{T} allows you to use rows instead. See the "Related Commands" section for the commands that this is useful for.

# Related Commands

- augment(
- cumSum(
- Matr►list(
- rowSwap( (and other row operations)

.