Some definitions:

Linear algebra is a systematic exploration of linear equations and is related to a new kind of arithmetic called the arithmetic of matrices
Linear algebra involves using a variety of methods for finding solutions to linear systems
- But linear algebra isn't exclusively about solving linear systems; the tools of matrices and vectors have a whole wealth of applications
Linear algebra is about translating something residing in an m-dimensional space into a corresponding shape in an n-dimensional space

Fundamentals -> vectors -> matrices -> linear transformations -> eigenvalues and eigenvectors

Linear equation

An equation where two mathematical expressions are defined as being equal. If an equation contains an argument of trigonometric, exponential, logarithmic or hyperbolic functions, then the equation is not linear
A finite number of linear equations with a finite number of unknowns is called a system of linear equations or a linear system

Links