New notation dedicated to higher education linear algebra instructors: product between a vector and a family of vectors

Abstract

This article presents a new mathematical concept called the external scalar product of a matrix by a family of vectors. This new product is important when the property to be demonstrated concerns the family and is no longer the nature of its vector. This is analogous to the integration technique by substitution, where the variable of integration is changed to simplify the calculation. Thanks to this product, we have discovered a deletion method that has very interesting applications in the teaching of linear algebra. The primary objective of this tool is to simplify the teaching of several concepts in linear algebra.