论文标题
如何构建一个满足二次多项式方程的上三角矩阵
How to construct a upper triangular matrix that satisfy the quadratic polynomial equation with different roots
论文作者
论文摘要
令$ r $为具有身份$ 1 $的协会戒指。我们描述了$ t_n（r）$中的所有矩阵，$ n $ n $上三角矩阵（$ r $（$ n \ in \ mathbb {n} $））和$ t _ {\ infty}（r）$无限上限三角形矩阵$ r $ r $ $ r $ $ r $ nogy $ s nogial poty y y y y y y quadial y y y y y y y y y y y y 2对于这样的建议，我们假设上述多项式在$ r $中具有两个不同的根。此外，在有限的$ r $中，我们计算求解矩阵方程$ a^2-ra+si = 0的所有矩阵的数量，其中$ i $是身份矩阵。
Let $R$ be an associative ring with identity $1$. We describe all matrices in $T_n(R)$ the ring of $n\times n$ upper triangular matrices over $R$ ($n\in \mathbb{N}$), and $T_{\infty}(R)$ the ring of infinite upper triangular matrices over $R$, satisfying the quadratic polynomial equation $x^2-rx+s=0$. For such propose we assume that the above polynomial have two different roots in $R$. Moreover, in the case that $R$ in finite, we compute the number of all matrices to solves the matrix equation $A^2-rA+sI=0,$ where $I$ is the identity matrix.
