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Why are orthogonal matrices important?

- Thread starter matqkks
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Why are orthogonal matrices important?

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2) Orthogonal matrices have a great numerical stability. Multiplying with an orthogonal matrix causes almost no errors. Furthermore, there are a lot of decomposition theorems involving orthogonal matrices. For example the singular value decomposition.

3) Orthogonal matrices correspond to the linear isometries. So from a categorical point of view, they are the isomorphisms of normed vector spaces. We often identify between spaces if they are the same up to linear isometry.

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