The transpose of a matrix is when you turn all the rows of a matrix into columns and vice versa. Row 1 becomes column 1, row 2 becomes column 2, and so on. The transpose of a matrix, A, is denoted

A^T.

When you transpose a matrix, the element in row i, column j becomes the element in row j, column i of the transposed matrix.

Let’s see some examples to better understand what the transpose of a matrix is.

First example (

click here):

1. Turn the rows into columns

Next example (

click here):

1. Turn the rows into columns

Last example (

click here):

1. Turn the rows into columns

This concept can be hard to visualize, so practicing a few examples will help you understand and become familiar with the transpose of a matrix. For more help or practice on the transpose of a matrix and other related matrix topics, visit Symbolab’s

Practice.

Until next time,

Leah

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