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Linear Algebra

How to find the eigenvalues of a matrix?

We learn to you how to find the eigenvalues of a matrix as well as the associated eigenvectors. This notion...

Hyperplane linear subspace

In this article, we define and give some exercises with answers on the hyperplane linear subspace. For instance, a hyperplane...

Linear transformations and matrices

We introduce in a simple way the concept of linear transformations and matrices. there is a deep connection between a...

Matrix Operations

One of the most important courses in linear algebra is matrix calculus.  We discuss matrix operations, mainly the multiplication of...

Direct sum of subspaces examples

The philosophy behind the direct sum of subspaces is the decomposition of vector spaces as a sum of disjoint spaces....

Matrix trace worksheet

A matrix trace is a scaler attached to a matrix that gives quick insights into matrix regularities such as similarity...

Vector spaces exercises

We provide vector spaces exercises with detailed answers. Such spaces are natural in mathematics in which we can manipulate computation...