# What is the square of a column vector?

## Homework Statement

Hi,

Is there a matrix property that can be applied to take the square of a column vector?

Something like:

${\bf x}=\left[x_1,x_2,x_3\right]^T$
$\left[{\bf x}\right]^2$
$={\bf x}{\bf x}^T$
or
$={\bf x}^T{\bf x}$?

Thank you.

## The Attempt at a Solution

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SammyS
Staff Emeritus
Homework Helper
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## Homework Statement

Hi,

Is there a matrix property that can be applied to take the square of a column vector?

Something like:

${\bf x}=\left[x_1,x_2,x_3\right]^T$
$\left[{\bf x}\right]^2$
$={\bf x}{\bf x}^T$
or
$={\bf x}^T{\bf x}$?

Thank you.
...
What is the size of the matrix: $={\bf x}{\bf x}^T\,?$

What is the size of the matrix: $={\bf x}^T{\bf x}\,?$

Hi SammyS,

${\bf x}{\bf x}^T$ is 3x3
while
${\bf x}^T{\bf x}$ is 1x1

I'm not sure what you mean by the square of a column vector...

SammyS
Staff Emeritus