Linear Algebra and the C Language/a08z


A change of basis consists of converting every assertion expressed in terms of coordinates relative to one basis into an assertion expressed in terms of coordinates relative to the other basis... Wikipedia: Change of basis


Change of basis with invertible matrices:

  Let B, the matrix for the change of basis for the basis B

a) Find the coordinates of U in standard basis:

                                       B * U_b = U_s          *

b) Find the coordinates of U in basis B: 

                                      invB U_s = U_b 

                   We have:            B * U_b = U_s          *                             
Let's use the inverse of B:       invB B * U_b = invB U_s
      We have U in basis B:                U_b = invB U_s

Exemples d'applications :

a) Example b) Example

Change of basis with non-invertible matrices:

  Let B, the matrix for the change of basis for the basis B

a) Find the coordinates of U in standard basis:

                             B U_b = U_s           

b) Find the coordinates of U in basis B: 

 You must create the system and resolve it:
 
              You have:      B U_b = U_s
   You can introduce X:      B  X  = U_s
  
  To find X you must resolve the system B|U_s = X = U_b


Exemples d'applications :

a) Example b) Example
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