Trace and Spectrum of Scalar-Involutory Matrices and Scalar-Anti-Involutory Matrices
By applying the invariant properties of eigenvalues and traces under the similar relationship,and avoiding solving characteristic polynomials,the calculation formulas for eigenvalues and determinant of the scalar-involutory matrices and scalar-anti-involutory matrices,and the similar equivalence classes of the corresponding matrices determined by the trace are shown.As an application,the related conclusions of the usual involutory matrices,anti-involutory matrices,symmetric orthogonal matrices,and anti-symmetric orthogonal matrices are obtained.
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维普
