Abstract: This paper is a continuation of my paper〔1〕.
Let A= (a_ij be a sguare marix of order n and λ₁, λ₂, …λn its characterstic roots. We define the trace \textt_\textr \textA=\sum\limits_1-1^\textn \texta_\texti j and the modusus. \|\textA\|=\left(\sum\limits_\texti, j=1^\textn\left|\texta_\texti j\right|^2\right)^\frac12 In the present paper We shall prove the theorem as follows: \;\;\;\;\;\;\;\;\;\;\;\;\textt_\textr \textA^2 \textK=\left\|\frac\textA^\textK+\textA^\textK*2\right\|^2-\| \frac\textA^\textK-\textA^\textK*2 \texti \\ +\frac\texti2\left(\left\|\frac\textA^\textK+\textA^\textK*2+\frac\textA^\textK-\textA^\textk*2 \texti\right\|^2-\left\|\frac\textA^\textk+\textA^\textk*2-\frac\textA^\textk-\textA^\textk *2 \texti\right\|^2\right) Where A* is the conjugate of the transpose of A and K may assume any in tegral value.