论文标题
接近线性代数
Near-linear algebra
论文作者
论文摘要
在本文中，我们证明，近矢量空间的世界使我们能够解决非线性问题，但是可以访问线性代数必须提供的大多数工具。我们为将经典的线性代数扩展到近线性代数的近距离空间建立了一些基本结果。在本文中，我们最终确定了代数证明，在加法和标量乘法下，任何非空的$ f $ -subspace稳定性都是$ f $ -subspace。我们证明，$ f $ -subspace的近矢量空间的任何商都是近矢量空间，也是第一个近矢量空间的同构定理。为此，我们获得了跨度的基本描述。在准内核之外定义线性独立性，我们证明近矢量空间是根据标量基础的存在来表征的，我们获得了一个新的重要基础概念。
In this paper, we prove that the world of near-vector spaces allows us to work with non-linear problems and yet, gives access to most of the tools linear algebra has to offer. We establish some fundamental results for near-vector spaces toward extending classical linear algebra to near-linear algebra. In the present paper, we finalize the algebraic proof that any non-empty $F$-subspace stable under addition and scalar multiplication is an $F$-subspace. We demonstrate that any quotient of a near-vector space by an $F$-subspace is a near-vector space and the First Isomorphism Theorem for near-vector spaces. In doing this, we obtain fundamental descriptions of the span. Defining linear independence outside the quasi-kernel, we prove that near-vector spaces are characterized in terms of the existence of a scalar basis, and we obtain a new important notion of basis.
