Two $n\times n$ complex matrices $A$ and
$B$ are said to be consimilar if ${S^{-1}}A\overline S=B$ for some
nonsingular $n\times n$ complex matrix $S$. This paper, by means
of real representation of a complex matrix, studies problems of
reducing a given $n\times n$ complex matrix $A$ to triangular or
diagonal form by consimilarity, not only gives necessary and
sufficient conditions for contriangularization and
condiagonalization of a complex matrix, but also derives an
algebraic technique of reducing a matrix to triangular or diagonal
form by consimilarity.