How to check if a matrix is orthogonal?
Understand the Problem
The question is asking for the process or method to determine if a given matrix is orthogonal. An orthogonal matrix is one where the rows and columns are orthogonal unit vectors, which can be checked by confirming that the transpose of the matrix is equal to its inverse.
Answer
Compute the transpose, multiply by the original matrix, and check if the product is the identity matrix.
To check if a matrix is orthogonal, compute its transpose, multiply the original matrix by the transpose, and verify if the result is the identity matrix.
Answer for screen readers
To check if a matrix is orthogonal, compute its transpose, multiply the original matrix by the transpose, and verify if the result is the identity matrix.
More Information
Orthogonal matrices have the special property that their inverse is equal to their transpose.
Tips
Ensure that the matrix is square before checking for orthogonality; non-square matrices cannot be orthogonal.
Sources
- Orthogonal Matrix (Definition, Properties with Solved Examples) - byjus.com
- Linear Algebra : Orthogonal Matrices - Varsity Tutors - varsitytutors.com
- How to identify an orthogonal(orthonormal matrix)? - math.stackexchange.com
