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# Savings due to zeros pt1

Consult pt2 here.

In this post I will provide a journal about the savings due to the presence of zeros in the submatrix needed to compute the sum rules.

Day 0

Problems found regarding the savings. The $${\rm det}$$ and a transformation are not always valid. Sometimes, the submatrix is not Hessenberg.

Day 1

$T_{U, V}^{\lambda}= \frac{1}{\sqrt{\Theta_{i}^{f}}} \frac{1}{\sqrt{\Theta_{j}^{g}}} \sum_{\cup_\gamma S_{\alpha} \gamma S_{\beta}=S_{n}}\left(\sum_{\sigma \in S_{\alpha} \gamma S_{\beta}} \omega_{i, j}^{\lambda}(\sigma)\right) X_{f\circ\gamma, g}.$

According to the previous equation, if the submatrix present some zeros then at least one $$X_{f\circ\gamma, g}$$ is zero. This in turn leads to avoiding compute some orthogonal irrep (OI) entries.

This is the unique saving I see at the present.

Thanks to Antti Koskinen Post