21. The finite-dimensional spectral theorem says that any symmetric matrix whose entries are diagonalized by an orthogonal matrix . 22. An orthogonal matrix " A " is necessarily reflection, or a composition of reflection and rotation. 23. An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of " 1. 24. The problem of finding the orthogonal matrix Q nearest a given matrix M is related to the Orthogonal Procrustes problem. 25. Dividing " H " through by this length gives an orthogonal matrix whose transpose is thus its inverse. 26. Any orthogonal matrix of size can be constructed as a product of at most " n " such reflections. 27. But surely by my argument, an orthogonal matrix cannot have an eigenvalue that isn't plus or minus one? 28. Where " A " is a 2? orthogonal matrix and is an arbitrary ordered pair of numbers; that is, 29. In Lie group terms, this means that the Lie algebra of an orthogonal matrix group consists of skew-symmetric matrices. 30. As another example, with appropriate normalization the discrete cosine transform ( used in MP3 compression ) is represented by an orthogonal matrix .
