How Do You Compute the Tensor Product of Two Matrices?

[Funzies]

Homework Statement

If A = \[ \left( \begin{array}{ccc}<br /> a &amp; b \\<br /> c &amp; d \end{array} \right)\][\tex]<br /> and B=\[ \left( \begin{array}{ccc}&lt;br /&gt; \alpha &amp;amp; \beta \\&lt;br /&gt; \gamma &amp;amp; \delta \end{array} \right)\] [\tex]&lt;br /&gt; in the basis |e1&amp;gt;,|e2&amp;gt;, find&lt;br /&gt; AxB (where &amp;quot;x&amp;quot; is the tensorproduct) in the basis |e1e1&amp;gt;,|e1e2&amp;gt;,|e2e1&amp;gt;,|e2e2&amp;gt;&lt;br /&gt; &lt;br /&gt; &lt;h2&gt;Homework Equations&lt;/h2&gt;&lt;br /&gt; -&lt;br /&gt; &lt;br /&gt; &lt;h2&gt;The Attempt at a Solution&lt;/h2&gt;&lt;br /&gt; I managed to find out how the new matrix works :&lt;br /&gt; C = \[ \left( \begin{array}{ccc}&amp;lt;br /&amp;gt; a11B &amp;amp;amp; a12B \\&amp;lt;br /&amp;gt; a21B &amp;amp;amp; a22B \end{array} \right)\]&lt;br /&gt; I&amp;#039;ve been trying to find a formula, expressed in indices voor the C_{ij}[\tex] element, but I can&amp;amp;#039;t seem to work it out. I am able to find the C_{43} element in this expample, but I can&amp;amp;#039;t generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; EDIT: Latex is acting really weird, all the formulas are in the wrong places?!

 

[Funzies]

Homework Statement

If A = \[ \left( \begin{array}{ccc}<br /> a &amp; b \\<br /> c &amp; d \end{array} \right)\]
and B=\[ \left( \begin{array}{ccc}<br /> \alpha &amp; \beta \\<br /> \gamma &amp; \delta \end{array} \right)\]
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 = \[ \left( \begin{array}{ccc}<br /> a11B &amp; a12B \\<br /> a21B &amp; a22B \end{array} \right)\]
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 A = \[ \left( \begin{array}{ccc}<br /> a &amp; b \\<br /> c &amp; d \end{array} \right)\][\tex]<br /> and B=\[ \left( \begin{array}{ccc}&lt;br /&gt; \alpha &amp;amp; \beta \\&lt;br /&gt; \gamma &amp;amp; \delta \end{array} \right)\] [\tex]&lt;br /&gt; in the basis |e1&amp;gt;,|e2&amp;gt;, find&lt;br /&gt; AxB (where &amp;quot;x&amp;quot; is the tensorproduct) in the basis |e1e1&amp;gt;,|e1e2&amp;gt;,|e2e1&amp;gt;,|e2e2&amp;gt;&lt;br /&gt; &lt;br /&gt; &lt;h2&gt;The Attempt at a Solution&lt;/h2&gt;&lt;br /&gt; I managed to find out how the new matrix works :&lt;br /&gt; C = \[ \left( \begin{array}{ccc}&amp;lt;br /&amp;gt; a11B &amp;amp;amp; a12B \\&amp;lt;br /&amp;gt; a21B &amp;amp;amp; a22B \end{array} \right)\]&lt;br /&gt; I&amp;#039;ve been trying to find a formula, expressed in indices voor the C_{ij}[\tex] element, but I can&amp;amp;#039;t seem to work it out. I am able to find the C_{43} element in this expample, but I can&amp;amp;#039;t generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; EDIT: Latex is acting really weird, all the formulas are in the wrong places?!

 

[Funzies]

If A = \[ \left( \begin{array}{ccc}<br /> a &amp; b \\<br /> c &amp; d \end{array} \right)\][\tex]<br /> and B=\[ \left( \begin{array}{ccc}&lt;br /&gt; \alpha &amp;amp; \beta \\&lt;br /&gt; \gamma &amp;amp; \delta \end{array} \right)\]<br /> in the basis |e1&gt;,|e2&gt;, find<br /> AxB (where &quot;x&quot; is the tensorproduct) in the basis |e1e1&gt;,|e1e2&gt;,|e2e1&gt;,|e2e2&gt;<br /> <br /> I managed to find out how this new matrix works :<br /> C = \[ \left( \begin{array}{ccc}&lt;br /&gt; a11B &amp;amp; a12B \\&lt;br /&gt; a21B &amp;amp; a22B \end{array} \right)\]<br /> I&#039;ve been trying to find a formula, expressed in indices voor the C_{ij} element, but I can&#039;t seem to work it out. I am able to find the C_{43} element in this expample, but I can&#039;t generalise it to a matrix of arbritary sizes and a arbritary element. Can anyone help me with this?

 

[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.