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