11. When Q = 0 the second condition requires that O is an orthogonal matrix . 12. It is orthostochastic if there exists an orthogonal matrix " O " such that 13. In this case, because and are real valued, they each are an orthogonal matrix . 14. In components, such operator is expressed with orthogonal matrix that is multiplied to column vectors. 15. Stronger than the determinant restriction is the fact that an orthogonal matrix can always be modulus 1. 16. A direct isometry is an affine transformation with an orthogonal matrix that has a determinant of 1. 17. A general orthogonal matrix has only one real eigenvalue, either + 1 or " 1. 18. Here the image \ rho ( z ) of z = x + iy is the orthogonal matrix 19. For a stable method of converting an orthogonal matrix to a quaternion, see Rotation matrix # Quaternion. 20. In similarity transformation, i . e . a product of an orthogonal matrix and a scalar matrix.
