math数学 - 随笔分类(第2页) - papering

确界原理 supremum and infimum principle 戴德金定理 Dedekind theorem

摘要：确界原理 supremum and infimum principle 戴德金定理 Dedekind theorem http://www.math.ubc.ca/~cass/courses/m446-05b/dedekind-book.pdf#page=15 continulity and irr 阅读全文

posted @ 2019-04-02 09:03 papering 阅读(650) 评论(0) 推荐(0)

Abhyankar's Conjecture

摘要：http://www.math.purdue.edu/about/purview/spring95/conjecture.html A Layman's Perspective of Abhyankar's Conjecture by Ganapathy Sundaram Consider a po 阅读全文

posted @ 2019-03-29 15:48 papering 阅读(245) 评论(0) 推荐(0)

algebraically closed field 代数闭域

摘要：algebraically closed field https://en.wikipedia.org/wiki/Algebraically_closed_field As an example, the field of real numbers is not algebraically clos 阅读全文

posted @ 2019-03-29 15:01 papering 阅读(972) 评论(0) 推荐(0)

怎么表示自然数陶哲轩

摘要：数学严谨阅读全文

posted @ 2019-03-28 18:41 papering 阅读(202) 评论(0) 推荐(0)

拓扑学家不能区分咖啡杯和甜甜圈，这是因为一个足够柔软的甜甜圈可以捏成咖啡杯的形状

摘要：https://zh.wikipedia.org/wiki/同胚阅读全文

posted @ 2019-03-27 11:35 papering 阅读(2908) 评论(0) 推荐(0)

manifold 微分流形上可以定义可微函数、切向量、切向量场、各种张量场等对象并建立其上的分析学，并可以赋予更复杂的几何结构以研究它们的性质。

摘要：小结： 1、流形（英语：Manifolds）一般可以通过把许多平直的片折弯并粘连而成，是局部具有欧几里得空间性质的空间，是欧几里得空间中的曲线、曲面等概念的推广 2、描述一个流形往往需要不止一个“地图”，因为一般来说流形并不是真正的欧几里得空间。举例来说，地球就没法用一张平面的地图来合适地描绘。 h 阅读全文

posted @ 2019-03-27 09:44 papering 阅读(1837) 评论(0) 推荐(0)

Rodrigues Formula

摘要：https://en.wikipedia.org/wiki/Rodrigues%27_formula https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula 旋转阅读全文

posted @ 2019-03-26 16:52 papering 阅读(528) 评论(0) 推荐(0)

transformations 变换集合关系仿射变换

摘要：http://groups.csail.mit.edu/graphics/classes/6.837/F03/lectures/04_transformations.ppt https://groups.csail.mit.edu/graphics/classes/6.837/F03/lecture 阅读全文

posted @ 2019-03-26 11:04 papering 阅读(533) 评论(0) 推荐(0)

Canonical form

摘要：https://en.wikipedia.org/wiki/Canonical_form#Linear_algebra Suppose we have some set S of objects, with an equivalence relation R. A canonical form is 阅读全文

posted @ 2019-03-25 14:49 papering 阅读(564) 评论(0) 推荐(0)

Underdetermined system Constraint counting Overdetermined system

摘要：https://en.wikipedia.org/wiki/Underdetermined_system https://en.wikipedia.org/wiki/Constraint_counting In mathematics, constraint counting is counting 阅读全文

posted @ 2019-03-25 09:07 papering 阅读(456) 评论(0) 推荐(0)

LU decomposition can be viewed as the matrix form of Gaussian elimination.

摘要：https://en.wikipedia.org/wiki/LU_decomposition One way to find the LU decomposition of this simple matrix would be to simply solve the linear equation 阅读全文

posted @ 2019-03-25 08:59 papering 阅读(242) 评论(0) 推荐(0)

有限域伽罗瓦域

摘要：小结 1、根的置换：这些根所满足的任何代数方程，在置换之后也依然成立。 2、 x^3-2=0在Q上无解，域扩张field extension至R？》求x在fieldA上f(x)=0的解，(注意，讨论解一定要指明讨论的域field) >放到扩张域fieldB上讨论因为是更大的域，所以，在小域上解与解阅读全文

posted @ 2019-03-22 23:29 papering 阅读(1718) 评论(0) 推荐(0)

block diagonal matrix 直和块对角矩阵不完美有缺陷缩放射影几何

摘要：小结： 1、block diagonal matrix 直和块对角矩阵 A block diagonal matrix is a block matrix that is a square matrix, and having main diagonal blocks square matrice 阅读全文

posted @ 2019-03-21 16:43 papering 阅读(2481) 评论(0) 推荐(0)

Eisenstein's criterion

摘要：https://en.wikipedia.org/wiki/Eisenstein%27s_criterion In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integ 阅读全文

posted @ 2019-03-20 23:47 papering 阅读(372) 评论(0) 推荐(0)

理想

摘要：人生理想倍式拼凑不理想阅读全文

posted @ 2019-03-20 20:49 papering 阅读(176) 评论(0) 推荐(0)

invariant theory 不变量理论

摘要：https://baike.baidu.com/item/不变量理论/9224903?fr=aladdininvariant theory 一组几何元素由 k个参数组成的向量 P1表示．若 T为某一变换，T∈G ， G为某一变换群，这组几何元素经 T变换后，其参数组成的向量由 P1变为 P2(P1, 阅读全文

posted @ 2019-03-20 08:49 papering 阅读(1021) 评论(0) 推荐(0)

格拉姆矩阵合同矩阵

摘要：https://baike.baidu.com/item/格拉姆矩阵/16274086 https://en.wikipedia.org/wiki/Gramian_matrix https://en.wikipedia.org/wiki/Matrix_congruence https://en.wi 阅读全文

posted @ 2019-03-19 17:07 papering 阅读(1460) 评论(0) 推荐(0)

同余关系等价关系同余关系的原型

摘要：小结： 1、同余关系或简称同余是相容于某个代数运算的等价关系。 https://baike.baidu.com/item/同余关系 https://en.wikipedia.org/wiki/Congruence_relation https://en.wikipedia.org/wiki/Equi 阅读全文

posted @ 2019-03-19 16:32 papering 阅读(4555) 评论(0) 推荐(0)

同态同构

摘要：https://baike.baidu.com/item/同态假设M，M′是两个乘集，也就是说M和M′是两个各具有一个封闭的具有结合律的运算*与*‘的代数系统。σ是M射到M′的映射，并且任意两个元的乘积的像是这两个元的像的乘积，即对于M中任意两个元a、b，满足σ(a*b)=σ(a)*’σ(b)；也阅读全文

posted @ 2019-03-19 16:28 papering 阅读(990) 评论(0) 推荐(0)

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in

摘要：https://en.wikipedia.org/wiki/Congruence_relation In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an a 阅读全文

posted @ 2019-03-19 15:50 papering 阅读(260) 评论(0) 推荐(0)

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随笔分类 - math数学