Commit 8cca001e authored by velleto's avatar velleto
Browse files

Lecture 2019-02-08: Fixed mathematical error.

parent cca2305c
......@@ -163,8 +163,9 @@ To convince ourselves that this is true, we can multiply back:
& = \sum _j \sigma _k (a_j) \sigma _i (w_j) \\
& = (\sigma _k \circ \sigma _k ^{-1})(\sum _j \sigma _k (a_j) \sigma _i (w_j)) \\
& = \sigma _k (\sum _j a_j (\sigma _k ^{-1} \circ \sigma _i) (w_j)) \\
& = \sum _j a_j \sigma _{i'} (w_j) \\
& = (Ma)_{i'} \\
& = \sigma _k (\sum _j a_j \sigma _{i'} (w_j)) \\
& = \sigma _k ((Ma)_{i'}) \\
& = \sigma _k (0) \\
& = 0
\end{align*}
As the kernel is a subspace, we can take the difference $a - a' \in \mathrm{Ker}(M)$.
......
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