摘要
Motivation of this paper is an open problem exposed by B. Beauzamy .Let M be a 3×3 matrix and d(M) is the distance to the diagonal algebra. Let α(M)= sup {‖P ⊥MP‖∶P is a projection in the diagonal algebra} and then call K(M)=d(Μ)α(M) the distance coefficient of M. The following results are obtained: (1) If M has two zero entries apart from its diagonal, then K(M)322; (2) If M has one zero entry apart from its diagonal, then K(M)4132; (3) If M is arbitrary, then K(M)32.
Motivation of this paper is an open problem exposed by B. Beauzamy .Let M be a 3×3 matrix and d(M) is the distance to the diagonal algebra. Let α(M)= sup {‖P ⊥MP‖∶P is a projection in the diagonal algebra} and then call K(M)=d(Μ)α(M) the distance coefficient of M. The following results are obtained: (1) If M has two zero entries apart from its diagonal, then K(M)322; (2) If M has one zero entry apart from its diagonal, then K(M)4132; (3) If M is arbitrary, then K(M)32.
