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  • intuition - What is the affine space and what is it for? - Mathematics . . .
    It may be more fruitful to compare groups of transformations Speaking of groups acting on a Cartesian space, with the analogous questions in parentheses: orthogonal transformations ("What is an inner product space?"), linear transformations ("What is a vector space?"), affine transformations ("What is an affine space?")
  • 仿射函数、线性函数的区别? - 知乎
    严格意义上讲区别只在于有没有截距。 首先如果你谷歌一下,谷歌就会告诉你仿射函数就是线性函数加平移。其实从名字上就可以看出来区别在于一个是线性映射,一个是仿射映射。 在学校里(尤其是中学)经常使用包含截距的ax+b(一阶多项式)表示线性函数,但是,从严格的数学意义上讲,它是
  • What are differences between affine space and vector space?
    An Affine space abstracts the affine combinations You can think of an affine combination as a weighted average, or a convex hull (if you limit the coefficients to be between 0 and 1)
  • 仿射函数这名字好深奥,但概念其实非常简单,为什么要取这个名字? - 知乎
    我整理一下我查到的资料: “仿射”这个词,翻译自英语affine,为什么会翻译出这两个字,我没查到。 英语affine,来自于英语affinity。英语词根fin来自于拉丁语finis,表示“边界,末端”,例如finish、final等单词。词头ad表示“去,往”,拼出名词affinity,本意为“接壤,结合”,用来指“姻亲,由于
  • Closed subset of an affine variety. . . is it affine?
    My naive understanding of this affine not affine business is that for an affine variety we can write down something like a global coordinate system (the coordinate ring), while for a general algebraic variety we have just local coordinates, ie we have many affines patched together in a way that cannot be described globally with the usual tools
  • 请问仿射集 (affine set)和仿射包(affine hull)有什么区别? - 知乎
    仿射集 (Affine Set)和仿射包 (Affine hull)是凸优化中常见的两个概念。 仿射集 仿射包 仿射集 对于集合 C ⊆ R n C \subseteq R^ {n} ,如果通过集合 C C 中任意两个点的 直线 仍在集合 C C 中, 那么称 C C 是仿射集, 换言之, ∀ x ∈ C, y ∈ C, θ ∈ R \forall x\in C, y \in C, \theta \in R
  • convex analysis - Are affineness and convexity equivalent . . .
    In reading about convex optimization, the author states that all convex sets are affine Are affineness and convexity equivalent? If I understand, both definitions incorporate the notion that a s
  • Inverse of transformation matrix - Mathematics Stack Exchange
    Note that M is a composite matrix built from fundamental geometric affine transformations only Show the initial transformation sequence of M, invert it, and write down the final inverted matrix of M


















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