Number of possible zero entries in orthogonal matrices

An interesting observation, but it doesn't pan out unfortunately! It already fails in dimension 3. Wikipedia has the following counterexample of a rotoinversion: $$ \begin{bmatrix} 0 & -0.8 & - 0.6 \\ 0.8 & -0.36 & 0.48 \\ 0.6&0.48&-0.64 \end{bmatrix} $$

(WolframAlpha agrees that this is indeed orthogonal, the example is from here)

Tags:

Linear Algebra

Matrices

Orthogonal Matrices

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