A square matrix $Q$ is said to be $J$-orthogonal if $$ Q^T J Q = J. $$ What are the implicit conditions on this matrix $J$? I believe $J$ is typically chosen to be a symmetric non-degenerate form, but what other conditions are there? I want to say that $J$ always squares to the identity, but is this an implicit assumption?
2026-04-02 18:39:52.1775155192
What are the implicit conditions underlying the $J$ matrices for $J$-orthogonal matrices?
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