Table 1 Multiplication operation in QI’s
\(\:.\) | \(\:1\) | \(\:-1\) | \(\:\varvec{i}\) | \(\:-\varvec{i}\) | \(\:\varvec{j}\) | \(\:-\varvec{j}\) | \(\:\varvec{k}\) | \(\:-\varvec{k}\) |
|---|---|---|---|---|---|---|---|---|
\(\:1\) | \(\:1\) | \(\:-1\) | \(\:i\) | \(\:-i\) | \(\:j\) | \(\:-j\) | \(\:k\) | \(\:-k\) |
\(\:-1\) | \(\:-1\) | \(\:1\) | \(\:-i\) | \(\:i\) | \(\:-j\) | \(\:j\) | \(\:-k\) | \(\:k\) |
\(\:\varvec{i}\) | \(\:i\) | \(\:-i\) | \(\:-1\) | \(\:1\) | \(\:k\) | \(\:-k\) | \(\:-j\) | \(\:j\) |
\(\:-\varvec{i}\) | \(\:-i\) | \(\:i\) | \(\:1\) | \(\:-1\) | \(\:-k\) | \(\:k\) | \(\:j\) | \(\:-j\) |
\(\:\varvec{j}\) | \(\:j\) | \(\:-j\) | \(\:-k\) | \(\:k\) | \(\:-1\) | \(\:1\) | \(\:i\) | \(\:-i\) |
\(\:-\varvec{j}\) | \(\:-j\) | \(\:j\) | \(\:k\) | \(\:-k\) | \(\:1\) | \(\:-1\) | \(\:-i\) | \(\:i\) |
\(\:\varvec{k}\) | \(\:k\) | \(\:-k\) | \(\:j\) | \(\:-j\) | \(\:-i\) | \(\:i\) | \(\:-1\) | \(\:1\) |
\(\:-\varvec{k}\) | \(\:-k\) | \(\:k\) | \(\:-j\) | \(\:j\) | \(\:i\) | \(\:-i\) | \(\:1\) | \(\:-1\) |
