Eye of depth (VII) -- Elementary Transformation of matrix (attachment: explanation of some mathematical models)

One 、 Introduction of elementary transformation

Gauss elimination

Two 、 The elementary transformation of the three matrices and the corresponding three elementary matrices , Standard of matrix

2.1 Elementary transformation of three matrices

2.2 example

2.3 Standard form of matrix

2.4 Three Elementary Matrices

The first is i Xing He j Line exchange
The second is i Line times k times
The third is j Line times k Times to the... Th i Go ahead

Lower left Q₁ To Q_j Is elementary line transformation ,Q_j To Q_i Is elementary column transformation

3、 ... and 、 Common properties of elementary transformation and another simple solution of matrix inverse matrix

3.1 Common properties

3.2 Simple solution of matrix inverse

Reversible matrix can be transformed into identity matrix by elementary row transformation

Four 、 Definition and properties of matrix rank

When calculating rank , Try to form a lower triangular matrix

5、 ... and 、 Number of solutions of linear equations

6、 ... and 、 The application of matrix rank in machine learning linear regression algorithm （ intermediate ）

Bloggers are seeing a = (x^Tx)^-1x^TY When , It suddenly occurred to me , I once gave a lesson plan to freshmen

This ：4-1 Prediction and regression

Very much alike , You can associate and learn
N < n I have to talk about it next time