If $G= GL(n,\mathbb{R})$ and $H= O(n)$ then why the orbit space $G/H$ is homeomorphic to the space of all upper triangular matrices with positive diagonal entries?(Here action of $H$ on $G$ is the usual matrix multiplication)
2026-02-23 02:42:21.1771814541
The orbit space GL(n,R)/O(n)
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This follows from the QR decomposition: every $M\in GL(n,\mathbb{R})$ can be written in one and only one way as $TQ$, where $T$ is upper triangular and $Q$ is orthogonal.