| 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.
|
