Matlab 指令集和原理

Matlab 指令集和原理

vector and matrix norms

       >> norm(X, p)  x for matrix, p for  p-norm (default is 2)

           

determinate, inverse and pseudoinverses

      >>det(D)  D for matrix for determinate (行列式)

          For a 2×2 matrix (2 rows and 2 columns):

         The determinant is:

|A| = ad - bc
"The determinant of A equals a times d minus b times c"

           >>inv(D) D for matrix for inverse

         
                                            
           >>pinv(E) E for matrix for pseudoinverse

Matrix powers and exponentials

          >>F^2 F for matrix


         >>F.^2 F for matrix


        >>sqrt(F) F for matrix


Eigenvalue and eigenVectors


         >>eig(g) G for matrix

We can rewrite the condition Av=v as (A−I)v=0 where I is the nn identity matrix. Now, in order for a non-zero vector v to satisfy this equation, A−I must not be invertible.

Otherwise, if A−I has an inverse, (A−I)−1(A−I)v v = = (A−I)−10 0 But we are looking for a non-zero vectorv.

That is, the determinant of A−I must equal 0. We call p()=det(A−I) the characteristic polynomial of A. The eigenvalues of A are simply the roots of the characteristic polynomial of A.

Data analysis
       >>min(Data)

      >>max(Data)

      >>std(Data)


his is the formu

la for Standard Deviation:


                                                

      >>cov(Data)


      >>corrcoef(Data)