How Do You Compute the Tensor Product of Two Matrices?

[Funzies]

Homework Statement

If [tex]A = \[ \left( \begin{array}{ccc}<br /> a & b \\<br /> c & d \end{array} \right)\][\tex]<br /> and [tex]B=\[ \left( \begin{array}{ccc}<br /> \alpha & \beta \\<br /> \gamma & \delta \end{array} \right)\] [\tex]<br /> in the basis |e1>,|e2>, find<br /> AxB (where "x" is the tensorproduct) in the basis |e1e1>,|e1e2>,|e2e1>,|e2e2><br /> <br /> <h2>Homework Equations</h2><br /> -<br /> <br /> <h2>The Attempt at a Solution</h2><br /> I managed to find out how the new matrix works :<br /> $$C = \[ \left( \begin{array}{ccc}<br /> a11B & a12B \\<br /> a21B & a22B \end{array} \right)\]$$<br /> I've been trying to find a formula, expressed in indices voor the [tex]C_{ij}[\tex] element, but I can't seem to work it out. I am able to find the $$C_{43}$$ element in this expample, but I can't generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?<br /> <br /> EDIT: Latex is acting really weird, all the formulas are in the wrong places?![/tex][/tex][/tex]

 

[Funzies]

Homework Statement

If $$A = \[ \left( \begin{array}{ccc}<br /> a & b \\<br /> c & d \end{array} \right)\]$$
and $$B=\[ \left( \begin{array}{ccc}<br /> \alpha & \beta \\<br /> \gamma & \delta \end{array} \right)\]$$
in the basis |e1>,|e2>, find
AxB (where "x" is the tensorproduct) in the basis |e1e1>,|e1e2>,|e2e1>,|e2e2>

The Attempt at a Solution

I managed to find out how the new matrix works :
$$C = \[ \left( \begin{array}{ccc}<br /> a11B & a12B \\<br /> a21B & a22B \end{array} \right)\]$$
I've been trying to find a formula, expressed in indices voor the $$C_{ij}$$ element, but I can't seem to work it out. I am able to find the $$C_{43}$$ element in this expample, but I can't generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?

EDIT: Latex is acting really weird, all the formulas are in the wrong places?!

Homework Statement

If [tex]A = \[ \left( \begin{array}{ccc}<br /> a & b \\<br /> c & d \end{array} \right)\][\tex]<br /> and [tex]B=\[ \left( \begin{array}{ccc}<br /> \alpha & \beta \\<br /> \gamma & \delta \end{array} \right)\] [\tex]<br /> in the basis |e1>,|e2>, find<br /> AxB (where "x" is the tensorproduct) in the basis |e1e1>,|e1e2>,|e2e1>,|e2e2><br /> <br /> <h2>The Attempt at a Solution</h2><br /> I managed to find out how the new matrix works :<br /> $$C = \[ \left( \begin{array}{ccc}<br /> a11B & a12B \\<br /> a21B & a22B \end{array} \right)\]$$<br /> I've been trying to find a formula, expressed in indices voor the [tex]C_{ij}[\tex] element, but I can't seem to work it out. I am able to find the $$C_{43}$$ element in this expample, but I can't generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?<br /> <br /> EDIT: Latex is acting really weird, all the formulas are in the wrong places?![/tex][/tex][/tex]

 

[Funzies]

If [tex]A = \[ \left( \begin{array}{ccc}<br /> a & b \\<br /> c & d \end{array} \right)\][\tex]<br /> and $$B=\[ \left( \begin{array}{ccc}<br /> \alpha & \beta \\<br /> \gamma & \delta \end{array} \right)\]$$<br /> in the basis |e1>,|e2>, find<br /> AxB (where "x" is the tensorproduct) in the basis |e1e1>,|e1e2>,|e2e1>,|e2e2><br /> <br /> I managed to find out how this new matrix works :<br /> $$C = \[ \left( \begin{array}{ccc}<br /> a11B & a12B \\<br /> a21B & a22B \end{array} \right)\]$$<br /> I've been trying to find a formula, expressed in indices voor the $$C_{ij}$$ element, but I can't seem to work it out. I am able to find the $$C_{43}$$ element in this expample, but I can't generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?[/tex]

 

[arkajad]

You may like to check http://mathworld.wolfram.com/KroneckerProduct.html"

Kronecker product is in a reverse order than tensor product.

 

[Fredrik]

EDIT: Latex is acting really weird, all the formulas are in the wrong places?!

You wrote \tex instead of /tex in a few places.