page 232 of the 4th edition states that lengths and angles don't change when multiplying by an orthogonal matrix (about half way down the page in bold). It's true that the rotation matrix, for example, preserves the vector's length, but it does change the angle as that is its purpose. Does anyone know why it is mentioned that angles don't change as a result of multiplication by an orthogonal matrix? In the definition in the blue box below this statement in bold, it only mentions preservation of vector lengths.

Thank you.

Question

page 232 of the 4th edition states that  lengths and angles don't change when multiplying by an orthogonal matrix (about half way down the page in bold). It's true that the rotation matrix, for example, preserves the vector's length, but it does change the angle as that is its purpose. Does anyone know why it is mentioned that angles don't change as a result of multiplication by an orthogonal matrix? In the definition in the blue box below this statement in bold, it only mentions preservation of vector lengths.

Thank you.