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What is the square of a column vector?

  • Thread starter devonho
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  • #1
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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:

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

Thank you.


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
SammyS
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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:

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

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

What is the size of the matrix: [itex]={\bf x}^T{\bf x}\,?[/itex]
 
  • #3
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Hi SammyS,

[itex]{\bf x}{\bf x}^T[/itex] is 3x3
while
[itex]{\bf x}^T{\bf x}[/itex] is 1x1
 
  • #4
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I'm not sure what you mean by the square of a column vector...
 
  • #5
SammyS
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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 .
 

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