Are the set of all symmetric matrices and orthogonal matrcises connected in $M_n(\mathbb{R})$ and $M_n(\mathbb{C})$?completely out of idea.plz help
symmetric and orthogonal matrices are connected?
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general-topology
1 Answers
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Consider the images of each set under the determinant map. Are either of the images connected?
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1@jacob, every vector space is path connected, so are syymm matrces.... – 2012-04-27