ON SOME CLASSES OF SMOOTH TRANSFORMATIONS IN THE SPACE OF SYMMETRIC MATRICES
Nikita Vasil'evich Ilyushechkin · Sbornik Mathematics · 1995
Let be the space of -dimensional real symmetric matrices. Two families of infinitely smooth transformations in are considered. First, the family of transformations having the following property: for any matrix and an orthogonal matrix such that is a diagonal matrix, is also a diagonal matrix. Second, the family of transformations such that the diagonal entries of the matrix are zero whenever the matrix is diagonal.Bibliography: 6 titles.