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Orthogonal matrix

| 🗖 nosplit | ↑ parent "Named matrix" | words: 138 | descendant words: 183 | descendants: 1
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Preserves the dot product. This implies that it preserves norm and angles.
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Implies determinant plus or minus 1. Converse not true. But the converse within is true.
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Set of all of them form the orthogonal group. It is a group since their determinant is not 0, so they have inverses.
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For these matrices, the inverses are the transposes. Or equivalently, the set of rows is orthonormal, and so is the set of columns.
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Ancestors

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