Are orthogonal matrices invertible?
Understand the Problem
The question is asking whether orthogonal matrices have the property of being invertible, which refers to whether there exists a matrix that can reverse the effect of the orthogonal matrix when multiplied with it.
Answer
Yes
Yes
Answer for screen readers
Yes
More Information
Orthogonal matrices are always invertible and their inverse is equal to their transpose. By definition, orthogonal matrices satisfy Q^TQ = I.
Tips
Students might confuse orthogonality with general invertibility properties. Always remember that orthogonality implies invertibility, but not all invertible matrices are orthogonal.
Sources
- Orthogonal Matrix (Definition, Properties with Solved Examples) - Byju's - byjus.com
- Orthogonal Matrix - an overview - ScienceDirect Topics - sciencedirect.com
- Orthogonal Matrix -- from Wolfram MathWorld - mathworld.wolfram.com
Thank you for voting!
