论文标题
方程式系统的解决方案AX = B和AX = 0使用几何代数的统一方法：外部产品应用和角度条件
Solution of Linear Systems of Equations Ax=b and Ax=0 using Unifying Approach with Geometric Algebra: Outer Product Application and Angular Conditionality
论文作者
论文摘要
方程式AX = B和AX = 0的线性系统的解决方案是许多计算软件包的重要组成部分。本文使用外产物（扩展的跨产品）基于欧几里得空间的投射扩展提供了一种新的制定。这种方法能够解决两种情况，即AX = B和AX = 0。所提出的方法实际上导致了线性系统的分析解决方案，以在使用数值评估之前可以应用其他向量操作的形式。 该贡献还提出了一种新方法，以估算适用于非方格矩阵的矩阵。如果使用几乎无限的精度，则将条件性分开为结构性条件，显示矩阵属性，数值问题取决于右侧影响（如果给出）数值表示。
A solution of linear systems of equations Ax=b and Ax=0 is a vital part of many computational packages. This paper presents a novel formulation based on the projective extension of the Euclidean space using the outer product (extended cross-product). This approach enables to solve the both cases, i.e. Ax=b and Ax=0. The proposed approach leads actually to an analytical solution of linear systems in the form on which the other vector operation can be applied before using the numerical evaluation. This contribution also proposes a new approach to the conditionality estimation of matrices applicable to non-squared matrices. It splits the conditionality to structural conditionality showing matrix property if nearly unlimited precision is used, numerical issue which depends on numerical representation with respect to the right-hand side influence, if given.
