Eigen-decomposition
给定方阵 $A$，如果 $\exists \lambda, \mathbf{v} \neq \mathbf{0}$ 满足 $A \mathbf{v} = \lambda \mathbf{v}$，我们称 $\lambda$ 是 $A$ 的一个 eigenvalue，$\mathbf{v}$ 是 $A$ 对应 $\l...
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Hadamard Product / Diagonal Matrix / Orthogonal Matrix
Hadamard Product
Tensor
参考：
Minimum vs Minimal w.r.t. generalized inequality
假定有一个 proper cone $K$，它定义了一个 generalized inequality 关系 $\preceq_K$。
Linear Independence / Affine Independence / Non-singular Square Matrix / Definite Square Symmetric Matrix
Linear Independence / Affine Independence
Digest of Terence Tao Analysis
Chapters
Infinite Cartesian Products
其实只是 Terence Tao 大神的定义写得稍微有一点绕，整体还是好理解的。
Topology Induced by Metric / Equivalence of Metrics
虽然 topology 的定义已经摆脱了 metric，但是这并不妨碍我们从 topology 的角度去研究 metric，这并不存在矛盾。
Topology / Topological Space / Redefine Neighborhood, Limit Point, Interior Point and Exterior Point
Topology / Topological Space
Neighborhood / Open Set / Continuity / Limit Points / Closure / Interior / Exterior / Boundary
Quoted from Analysis II by Victor Guillemin, MIT and Topology for dummies by Damian Giaouris, Newcastle University with modification.