In reading something about relativity and in particular looking at first to the definition of spacetime as "spherically symmetric" I have encountered the following notation referred to an element of the orthogonal special group of $\mathbb{R}^3$ ($SO(3)$): $$R\in SO(3)\iff \begin{cases} {}^{t}_{}R I R=I\\ det(R)=1 \end{cases} $$ What is the meaning of the superscript $t$? Which operation of matrices correspond?
2026-04-07 04:47:36.1775537256
Notation on definition of spherical symmetry of spacetime
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That superscript $^t$ is (bad, in my opinion) notation for the matrix transpose. That is, if $$R = \pmatrix{a & b & c \\ d & e & f \\ g & h & i}$$, then $^tR$ (urgh, the kerning) is simply the matrix $$\pmatrix{a & d & g\\b & e & h\\c & f & i}.$$