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What is an orthogonal matrix?

Updated: 4/28/2022
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14y ago

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A matrix A is orthogonal if itstranspose is equal to it inverse. So

AT is the transpose of A and A-1 is the inverse.

We have AT=A-1

So we have :

AAT= I, the identity matrix

Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal.

The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.

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