Generalized Inverses of Matrices and Its Applications.
Generalized Inverses of Matrices and Its Applications.
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发表时间：
1983-12
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通讯作者：
A. Doma
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作者：
A. Doma
文摘：讨论了具有多项式元素x，y，z.的矩阵的各种广义逆的理论和计算方法，等等，给出了本文给出了一个求常矩阵广义逆的简单算法，并将其应用于多元多项式矩阵的情形。给出了多元多项式元环上矩阵的Smith形式的约化。本文给出了研究系统Ax = B在A的秩为常数和非常数时的一个简单算法。研究了广义逆在求解更一般的矩阵方程如李雅普诺夫方程和黎卡提方程中的应用。（作者）
Abstract : Theory and computation techniques of the various type of generalized inverses of matrices which have polynomial elements x, y, z ..., etc., are presented. A simple algorithm for computation of generalized inverses of a constant matrix is established, and then applied to the case of matrices having polynomial elements in several variables. Reduction of a matrix to its smith form over the ring of polynomial elements in several variables is presented. A simple algorithm for investigation of the system Ax = b in case of constant and nonconstand rank of A is presented. Application of generalized inverses to solve more general matrix equations such as Lyapunov and Riccati equations is studied. (Author)