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[TOC] Definition(one contrast): linear combination of group mean vectors Φ=∑Gg=1cgμ^g\Phi = \sum_{g=1}^G c_g \hat\mu_g is a contrast if ∑Gg=1cg=0\sum_{g=1}^G c_g =0 Definition(two contrasts): two co

Centering data setApplication1. Centering data setIf we have a data set X∈Rn×pX\in \mathbb{R}^{n\times p}(each row is a sample), then column mean of this data set can be expressed in X¯=1nXT1n\bar

If we have two matrices, AA and BB with AA being positive definite and BB being positive semidefinite matrices.Firstly, from the eigen decomposition of AA, we know that there exists an orthogonal matri

matrix V scalarscalar V matrixvector V vectorexamples1 derivative of inverse matrix2 derivative of trace1. matrix V scalar∂A(x)∂x=[∂A(x)ij∂x]i,j\begin{equation}\frac{\partial A(x)}{\partial x} =

Minor余子式1 First Minor一阶余子式Cofactors代数余子式1 Cofactor expansion of the determinant2 Cofactor for computing inverse of a matrix1. Minor（余子式）In linear algebra, a minor of a matrix A is the determinant o

Definitions of continuousProperties of continuous1. Definitions of continuousDef 1: (continuous) Given a function f:X→Rf: X\rightarrow \mathbb{R}, ∀x0∈X\forall x_0 \in X, ∀ϵ>0\forall \epsilon >0, ∃ηx0

Convex and strictly convexStrong convex1. Convex and strictly convexCommon used notations about convexity are convex and strictly convex. Their definitions areDefinition 1: [convex]: f(x)f(x) is said

∇f(x)\nabla f(x) is L- Lipschitz continuous, then we have(1) ∥∇f(x)−∇f(y)∥2≤L∥x−y∥2\|\nabla f(x) - \nabla f(y)\|_2\leq L\|x-y\|_2(2) L2xTx−f(x)\frac{L}{2}x^T x - f(x) is convex(3) ∇2f(x)≤L⋅I\nabla ^

作者：Heinrich 链接：https://zhuanlan.zhihu.com/p/19763358 来源：知乎 著作权归作者 所有。商业转载请联系作者获得授权，非商业转载请注明出处。谨以此文献给大连海事大学的吴楠老师，柳晓鸣老师，王新年老师以及张晶泊老师。转载的同学请保留上面这句话，谢谢。如果还能保留文章来源就更感激不尽了。——更新于2014.6.6，想直接看更新的同学可以直接跳到第四