论文标题
匹配变量与无限线性方程系统中的方程式
Matching variables to equations in infinite linear equation systems
论文作者
论文摘要
线性代数的基本结果指出，如果同质线性方程系统仅具有微不足道的解决方案，那么最多有很多变量与方程式。我们证明了这种现象的以下概括。如果每个方程中具有有限多个变量有限的无限同质线性方程系统仅具有微不足道的解，则存在从变量到方程式的注入，将每个变量映射到其出现的方程式。
A fundamental result in linear algebra states that if a homogenous linear equation system has only the trivial solution, then there are at most as many variables as equations. We prove the following generalisation of this phenomenon. If a possibly infinite homogenous linear equation system with finitely many variables in each equation has only the trivial solution, then there exists an injection from the variables to the equations that maps each variable to an equation in which it appears.
