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I find it is not possible to “upload” the full journal. I receive an error about “too large”. Can you please help?
I have asked the same question in the traditional forum. I hope it is not too much of a bother.Q:
Why does the R operator span the algebra generated by {Re, Im, $i^2$}?
I’m reading Advanced calculus by K. Chandrasekharan. On page no. 142, he writes
$$\left(ax+byi\right)\left(cx+dyi\right) = acx^2+2adxyi+ady^2x+\left(bc+2bd\right)x+\left(ad-bc\right)y^2+\left(bd-ac\right)yi+bdy^2i+2bdi^2$$
He then concludes that the R-operator
$$
R=\begin{bmatrix}
0 & 1 & 0\\
0 & 0 & 1\\
0 & 0 & 0
\end{bmatrix}
$$
spans the algebra generated by $Re, Im, i^2$ by examining that the second column of the R-matrix is
$$
\begin{bmatrix}
0 & 1 & 0\\
0 & 0 & 1\\
0 & 0 & 0
\end{bmatrix}
$$
I can verify that the other two rows of the R-matrix are linear combinations of the form
\begin{bmatrix}
0 & 0 & 1\\
0 & 0 & 0\\
0 & 0 & 0
\end{bmatrix}
$$
and
$$
\begin{bmatrix}
0 & 0 & 0\\
0 & 0 & 1\\
0 & 0 & 0
https://colab.research.google.com/drive/1ndTGSElrhJE4H-mUihqBSnhye_jRfz7v
https://colab.research.google.com/drive/1kXdR9uYpjXnSA-v5q_CdS5d1kIYBDgjn
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https://colab.research.google.com/drive/19a9H4VwXHlrSQEJnwnTk29q12PQiM4zF
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