Linear Algebra

Within the project we have created digital materials to cover the standard topics of Linear Algebra:

• Vectors, lines and planes
• Vectors and scalars
• The inner product
• Cauchy-Schwarz and the triangle inequality
• The cross product
• Parametric and normal equations
• Systems of linear equations
• Solving linear systems
• Linear combinations and linear independence
• Linear combinations and linear span
• Linear independence
• Matrix operations
• Matrix algebra
• Matrix inverse
• Subspaces, basis and dimension
• Subspaces, null space and column space
• Basis
• Dimension
• Coordinate vectors
• Introduction to linear transformations
• Introduction and standard matrix
• Onto and one-to-one
• Determinants
• Computation
• Eigenvalues and eigenvectors
• Eigenvalues and eigenspace
• Similarity
• Geometric multiplicity and diagonalition
• Orthogonality
• Abstract vector spaces
• Linear transformations

The materials cover more or less the topics of some of the standard books like:

Linear Algebra and its Applications
Authors: David C. Lay, Steven R. Lay

The materials include short (interactive) videos explaining the theory, online interactive exercises, as well as a database of exam questions, to be used in print or online.

The materials have been used to compose various blended and online courses.

Two examples can be visited below. You can log in as guest, but notice that as guest, you do not have access to all functionalities. You can also use

Linear Algebra 1 is a first course on Linear Algebra