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We learn to you how to find the eigenvalues of a matrix as well as the associated eigenvectors. This notion is very useful because it makes it possible to simplify…

In this article, we define and give some exercises with answers on the hyperplane linear subspace. For instance, a hyperplane is a vector subspace of dimension equal to the dimension…

We introduce in a simple way the concept of linear transformations and matrices. there is a deep connection between a linear transformation and a matrix. In fact, using the basis…

One of the most important courses in linear algebra is matrix calculus.  We discuss matrix operations, mainly the multiplication of matrices. Indeed, matrices are widely used in IT. In fact,…

The philosophy behind the direct sum of subspaces is the decomposition of vector spaces as a sum of disjoint spaces. In fact, this is very important for defining the projections;…

A matrix trace is a scaler attached to a matrix that gives quick insights into matrix regularities such as similarity and other properties. We then propose to recall some properties…

We provide vector spaces exercises with detailed answers. Such spaces are natural in mathematics in which we can manipulate computation using the structure of these spaces. In such spaces, we…