Free online courseLinear Algebra Essentials

Course Description

Linear Algebra Essentials is a free online course in the School Subjects category, within Algebra, designed to build strong intuition for the ideas that power modern math, science, and computing. It guides you from the meaning of vectors and linear combinations to the geometric heart of span and basis, helping you see why these concepts matter rather than just how to compute them.

You will develop a clear understanding of linear transformations and how matrices represent them, including how composition naturally leads to matrix multiplication. The course highlights three-dimensional transformations and uses visuals to make determinants feel like a measure of scaling and orientation, connecting computation to geometry.

As you progress, you will explore inverse matrices, column space, and null space, along with the role of nonsquare matrices as dimension-changing transformations. The course also explains dot products through the lens of duality, then connects cross products to linear transformations to deepen conceptual clarity.

Later sections tie key problem-solving tools to geometric meaning, including Cramer’s rule and change of basis. You will also gain a practical, intuitive grasp of eigenvectors and eigenvalues, including a helpful shortcut for finding eigenvalues, and finish with a perspective on abstract vector spaces that unifies the ideas you have learned.

If you want a visually driven, intuition-first introduction that makes linear algebra click, this course provides a coherent path from fundamentals to the big-picture structure behind the calculations.