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## Main Question or Discussion Point

I've come here directly to the physics subforum for help understanding something.

https://www.physicsforums.com/showthread.php?p=4093403#post4093403

Now I am really confused: consider the matrix form of [tex]a^k[/tex] and calculate it all out we have

[tex]\begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 \\0 & 0 & 0 & -1 \end{pmatrix}\begin{pmatrix} 0 & 0 & 1 & 0 \\0 & 0 & 0 & -1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \end{pmatrix}[/tex]

A nullified matrix?

Have I got my [tex]a^k[/tex] matrix right... ?

I just don't understand why the relationship

[tex]\beta \alpha^k = \gamma^k[/tex]

would be important if it spat out a zero matrix, which makes me wonder strongly whether I even have the right conditions down for [tex]a^k[/tex]?

https://www.physicsforums.com/showthread.php?p=4093403#post4093403

Now I am really confused: consider the matrix form of [tex]a^k[/tex] and calculate it all out we have

[tex]\begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 \\0 & 0 & 0 & -1 \end{pmatrix}\begin{pmatrix} 0 & 0 & 1 & 0 \\0 & 0 & 0 & -1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \end{pmatrix}[/tex]

A nullified matrix?

Have I got my [tex]a^k[/tex] matrix right... ?

I just don't understand why the relationship

[tex]\beta \alpha^k = \gamma^k[/tex]

would be important if it spat out a zero matrix, which makes me wonder strongly whether I even have the right conditions down for [tex]a^k[/tex]?