Matrices et applications linéaires 4 - Changements de bases

Link to all course handouts: https://archive.org/details/@fran_ois... This video demonstrates how to transform a matrix representing a linear transformation in one basis into a matrix representing the same linear transformation in other bases. This leads, in particular, to the well-known relation A' = P^{-1}AP. This is one of the most important videos of the year because a central idea in linear algebra is that a good way to solve a problem is to work in a judiciously chosen basis, appropriate to the problem. 0:00 - Introduction and motivation 2:50 - Change-of-basis matrix 6:27 - Application exercise 10:19 - Inverse of a change-of-basis matrix 12:44 - Change of basis for an endomorphism 16:57 - For an AL (general case) 18:19 - Conjugation properties 20:44 - Similar matrices Video written and produced by François Giraud and Fanny Laignel.