# What is the square of a column vector?

1. Nov 20, 2011

### devonho

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

2. Nov 20, 2011

### SammyS

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

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

3. Nov 20, 2011

### devonho

Hi SammyS,

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

4. Nov 20, 2011

### murmillo

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

5. Nov 21, 2011

### SammyS

Staff Emeritus
Generally the square of a vector refers to the scalar product, which you can crudely think of as a 1 by 1 matrix. Therefore, the answer is (xT)x .