Sums of squares, the octonions, and (7,3,1) - MAA Sections
Sums of squares, the octonions, and (7,3,1) - MAA Sections
Sums of squares, the octonions, and (7,3,1) - MAA Sections
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The table as a matrix <strong>of</strong> signs <strong>of</strong> <strong>the</strong> e i<br />
. . . but looks are deceptive.<br />
⎡<br />
H =<br />
⎢<br />
⎣<br />
1 1 1 1 1 1 1 1<br />
1 −1 1 1 −1 1 −1 −1<br />
1 −1 −1 1 1 −1 1 −1<br />
1 −1 −1 −1 1 1 −1 1<br />
1 1 −1 −1 −1 1 1 −1<br />
1 −1 1 −1 −1 −1 1 1<br />
1 1 −1 1 −1 −1 −1 1<br />
1 1 1 −1 1 −1 −1 −1<br />
⎤<br />
⎥<br />
⎦<br />
Brown<br />
The Octonions