Applicazioni lineari (verifica)

In this video I present in a trivial way the concept of linear application, showing (using the definition) how to verify whether or not a law represents a linear application. Often in the exam topics of linear algebra applications (or functions) are assigned between two vector spaces and it is taken for granted that such applications are linear. It may happen that you are also asked to verify whether the application from one vector space to another given is linear, and in this case you must necessarily refer to the definition of linear application which at a practical level consists in verifying the two main properties. In the video in question after having stated the two properties that characterize a linear application, I have prepared a simple and very trivial example taking as a reference a function defined between two vector spaces on the field of real numbers and you will realize how simple it is to perform such checks. This verification is easily extendable even when the application is defined in spaces other than those of vectors, such as the vector space of matrices (over a generic field), or the vector space of polynomials of degree less than n, Enjoy the view. #salvoromeo #linearapplications #linearapplicationverification