Mathematical basis of artificial intelligence series of articles

  • 1. Mathematical basis of artificial intelligence —- derivative

  • 2. Mathematical basis of artificial intelligence —- matrix

  • 3. Mathematical basis of artificial intelligence —- Linear second-order approximation


Today review matrix, as a programmer, matrix in the application of the program must be more or less contact, especially in the image change algorithm on the application.

A, matrix

Definition 1.

Matrix is a set of complex numbers or real numbers arranged according to a rectangular array. It was originally derived from the square Matrix composed of coefficients and constants of equations. The concept was first put forward in the 19th century by British mathematician John Kelly. (This definition comes from Baidu Baike)

The following through a system of equations to declare a matrix (mathematical notation on PC writing is really very troublesome, do not know who has good formula notation writing software recommended below) :

A

2. Matrix operation

2.1. Matrix addition

A
B
A
B
A
B
B
A
A
B

A
B
A
B
B
So the conclusion is: when two matrices are added, the dimensions (the number of rows and columns) of the two matrices must be the same, such as either 2×2 or 3×3, etc.
A
B
C

2.2. Subtraction of matrices

A
B
A
B
B
A

2.3. Matrix multiplication

A
B
A
B

C
D
C
D
D
C
C
D
D
C

As you can see in the figure above, not just any two matrices can be multiplied, but only if A has the same number of columns as B has the same number of rows.

3. Identity matrix

Before introducing the identity matrix, let’s talk about what a square matrix is. As the name implies, a square matrix is a matrix with the same number of rows and columns, for example:

The identity matrix is a special square matrix. All its elements are composed of 0 and 1, and the diagonal element is 1, the rest elements are 0. Of course, the first-order identity matrix contains only one element 1: Iā‚ = [1].

I ā‚‚
I ā‚ƒ

I
A
A
A
I
A
A

A
I
A

4. The inverse matrix

A^-1
A
I
I
The inverse is equal to the reciprocal of the determinant of the matrix times the matrix
Adjoint matrix of
A
A
“Singular matrix”

(To be continued…)


Mathematical basis of artificial intelligence series of articles

  • 1. Mathematical basis of artificial intelligence —- derivative

  • 2. Mathematical basis of artificial intelligence —- matrix

  • 3. Mathematical basis of artificial intelligence —- Linear second-order approximation