A Note on Symmetric Matrices and Similarity.

Symmetric matrices play a vital role in many areas of applied as well as pure mathematics. Examples include the areas of linear statistical models and the theory of quadratic forms. The theory of similarity of matrices also has many applications for example, in differential equations, stochastic processes, and the solutions of matrix equations. Thus an interesting question which could prove to be of applied value is a question of the relationship of these two concepts When is a square matrix A over a field F similar over F to a symmetric matrix i.e., when does there exist a nonsingular matrix P over F such that P inverse AP is symmetric. In the present paper the author characterizes those fields F in which every square matrix over F is similar to a symmetric matrix.