The line image of the first lesson matrix and the column image (MIT public Lesson: Linear algebra) "reprint"

Reprinted from: http://blog.csdn.net/a352611/article/details/48602207

For personal notes only.

Directory (?) [-]

1. From a group of equations to a matrix
2. Row Picture Line Image
3. Column Picture columns image

This series of notes for the convenience of future self-check and write, more personal opinion, but also a study of review and Summary, Hope finish Bar ~

1. From the equation group to the matrix

The Matrix was born to express linear equations in a concise way.
Personal understanding is to better describe and resolve Ax = b
To understand from a system perspective:
A is our system.
X is our input.
b is our output.

2. Row Picture Line image

Matrix divided into row row and column columns
As the name implies, row picture concerns the line portion of the matrix

Line image can be obtained by drawing the equation represented by the line in straight line form
(Children's shoes should be very familiar with, from childhood to the university to teach this thinking)

3. Column Picture

Column picture focuses on the part of columns, and one column is a vector vectors

Now the problem is transformed in order to find a suitable linear combination(linear combination) that makes AX = b
The corresponding diagram

Vector b is a sum of two col vectors
Here again, when Vector x is taken, we can get the entire XY plane, meaning that whatever vector B can find the corresponding solution
(not when two col vectors are parallel)
* The practice of column picture does not seem to be emphasized in schools, but this understanding is more useful for mastering matrices and vectors

Then the teacher extended the 2D to 3D.
The approach and conclusion are the same, so when it is more difficult to describe it visually, the advantages of the matrix are reflected

So step by step we abstracted the essence of ax = b
Now that we have the concept of matrices , the next thing to do is to explore their properties and find the right algorithm to solve the problem.

PS: This picture is from the public class video

The line image of the first lesson matrix and the column image (MIT public Lesson: Linear algebra) "reprint"