- #1

SprucerMoose

- 62

- 0

Hi all,

I have been trying to gain a deeper insight into quadratic forms and have realized that my textbook makes the assumption that an orthogonal matrix corresponds to either a rotation and/or reflection when viewed as a linear transformation. The textbook outlines a proof that demonstrates all norms and dot products (and as a result angles) are invarient under such a transformation. Is this enough information to draw the conclusion that the transformation given by an orthogonal matrix is indeed a reflection/rotation or is there a more rigorous proof of this conjecture?

I have been looking around the interweb but havn't found anything as of yet.

I have been trying to gain a deeper insight into quadratic forms and have realized that my textbook makes the assumption that an orthogonal matrix corresponds to either a rotation and/or reflection when viewed as a linear transformation. The textbook outlines a proof that demonstrates all norms and dot products (and as a result angles) are invarient under such a transformation. Is this enough information to draw the conclusion that the transformation given by an orthogonal matrix is indeed a reflection/rotation or is there a more rigorous proof of this conjecture?

I have been looking around the interweb but havn't found anything as of yet.

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