Core concepts
vector spaces and geometry, linear combination, linear independence,
dimension, bases and change of basis, matrices and linear transformations, determinants,
equations of lines and planes in space, scalar product, orthogonality and orthonormality.
Applications
These concepts have applications across multiple fields. In programming, the terminology of one-dimensional and two-dimensional arrays is used to denote vectors and matrices. In computer graphics, equations of lines and planes in 2D and 3D, as well as matrices, are essential for image representation and transformation. In telecommunications, matrix theory underpins error detection and correction techniques (parity check, linear codes). Relevant applications also appear in graph theory, cryptography, and other scientific and technological areas.
Sample exercises
List of algebra exercises with step-by-step solutions.
[gd_projects category=”algebra-exercises” cols=”3″ per_page=”9″]
Matrix Rank in Python
<p>Three 3×3 cases to illustrate rank: identity (3), dependent rows (2) and dependent columns (1)</p>
