标题： 有限维向量空间基的规范形式 显示英文标题

标题： A normal form for bases of finite-dimensional vector spaces

摘要： 大多数构造有限维向量空间基的算法返回的基向量，除了正交性外，不表现出任何特殊性质。 虽然每个基都可以用来定义向量空间，但并非所有基都同样适合揭示待求解问题的特性。 本文引入了有限维向量空间基的一种规范形式，这可能在理解问题结构时非常有用，尤其是在基出现在解决过程中的一个步骤时。 这种规范形式可以看作是满列秩矩阵的一种新规范形式。 显示英文摘要

摘要： Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are equally suited to unravel properties of the problem to be solved. In this paper a normal form for bases of finite-dimensional vector spaces is introduced which may prove very useful in the context of understanding the structure of the problem in which the basis appears in a step towards the solution. This normal form may be viewed as a new normal form for matrices of full column rank.