Eye of depth (VI) -- inverse of matrix (attachment: some ideas of logistic model)

One 、 The introduction of matrix inverse and the definition of matrix inverse （*）

A^* Is the adjoint matrix , among A_ij by a_ij The algebraic covalent of

Different from definition 7 AB = BA = E, Make conditions popularize

Two 、 Calculation of matrix inverse

Block matrix （ Easy to calculate ）

3、 ... and 、 Common properties of matrix inverse , And the inverse of a special matrix

3.1 nature

|AB| = |A||B|
(AB)^-1=B^-1A^-1
(AB)^T=B^TA^T

3.2 The inverse of a special matrix

Four 、 Application of matrix inverse in machine learning linear regression algorithm ( primary )

N It's the number of samples ,a₁……a_n It's the parameter to be estimated

When bloggers see here , Suddenly I remembered that I once had a number of analog problems , Yes logistic Model , There was beta 1 To beta n The solution of , Bloggers didn't know how to solve , Now I understand , You should learn how to move on line
The model is introduced as follows ：

tearful , use matlab, Xiandai must study hard ！！！, The lesson of tears

5、 ... and 、 Block matrix

Transpose of block matrix , The whole is to transpose , Every small block should be transposed （ These two points should be kept in mind ）

5.1 Addition, subtraction and multiplication

5.2 Transpose operation and inverse operation

5.3 example

5.4 Calculation of covariance matrix