orthogonal matrix in a sentence

Examples

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