fancy words for academic papers

For vocabulary list,  please see the link below:
https://docs.google.com/spreadsheets/d/19aresbKpFTNOIe_6QjDZBN7iYNAMLCeqypFdRLmCUjc/edit?usp=sharing

IR related methods

LSI, PLSI, TransE,TransR Trans 系列：http://www.sohu.com/a/116866488_465975

linear algebra lecture 21 09/07/2017

特征值和特征向量

Ax = lamda*x
what are x and lamda for prpojection matrix
any x in the plane, Px = x ; lamda = 1
any x perpendicular to the plane, Px = 0x, lamda = 0

How to solve Ax = lamda * x

(A-lamda*I)*x = 0
A-lamda*I 一定要singular,不然没解
所以行列式为0

如果矩阵+3I, eigenvector don't change, eigen value +3

linear algebra lecture 20 08/28/2017

A-1 = 1/det(A)*Ct
C 是A的 余子式矩阵

克莱默法则
Ax=b
x=A-1b = > 1/det(A)*Ct*b
计算量超级大

行列式的值相当于某个物体的体积
detA = volume of a box
先从一个单位立方体开始 => det(cube) = 1
然后不同方向stretch. 或者变形之类的。可以看看其他的tutorial.

linear algebra lecture 18 & 19 08/27/2017

lecture 18
行列式 det A |A|
性质：
 1.
det I = 1
det singular matrix  = 0

2.
exchange rows reverse the sign of det.
det Permutation matrix = -1/ 1 根据单位矩阵来的

|a b
c d | = ad-bc

3.
|ta tb
c d| = t |a b; c d|

4. if two rows are equal, the det is 0.

5. subtract l*row i from row k. det doesn't change (消元的感觉)
6. row of 0s => det A = 0
7.三角矩阵的det 是对角线的乘积
8. det A = 0 if when A is singular
9.
det AB = detA*det B
det A-1 = 1/det A

det A2 = (det A)2
det 2A= 2^n*det A
(like a volume)

10. |At| = |A|
|Ut*Lt| = |LU|
=>|Ut|*|Lt| = |L|*|U|


lecture 19


det A = sum (A1aA2b...Anw)
如果 a,b...w可以通过偶数次变换成为1，2，。。。n 那就是正数，

余子式：行列式中指定一个数，去掉所在行和所在列的剩余矩阵是其中一个余子式
cofactor

linear algebra 08/23/2017 lecture 17

标准正交Q为什么好

QTQ = [q1t;q2t...]*[q1,12...]= [1,0...] 单元矩阵

projection matrix
P = Q(QtQ)-1Qt = QQt (=1 if Q is square)

gram-schmidt 正交化

conjugate prior

very nice resource:
http://www.cnblogs.com/lifegoesonitself/p/3423588.html