Linear Algebra and the C Language/a08z

__NOTOC__ 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: U_b = invB U_s We have: B * U_b = U_s (*) Let's use the inverse of B: invB B * U_b = invB U_s ID * 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 (B: non-invertible matrix) You must resolve the system: B|U_s (Give U in base b: U_b) Exemples d'applications : + a) Example b) Example