Mathematics II

What you'll learn

The key areas this subject covers, mapped to the official curriculum.

• Solve linear systems by Gaussian elimination, row reduction and LU factorization
• Model geometry and graphics using linear transformations and matrix algebra
• Work with vector spaces, bases, dimension, rank and change of basis
• Use eigenvalues, diagonalization, orthogonality and least squares in data and systems
• Reason about abstract algebraic structures - groups, subgroups, rings and fields

Course units

The structured path through this subject.

1. 1

   Linear Equations in Linear Algebra

   Systems of linear equations and the tools used to solve and analyse them.

   5 topics · 5 lessons available

2. 2

   Transformation

   Linear transformations and the matrices that describe them.

   4 topics · 4 lessons available

3. 3

   Matrix Algebra

   Matrix operations, inverses and factorizations.

   4 topics · 4 lessons available

4. 4

   Determinants

   Determinants, their properties and geometric meaning.

   3 topics · 3 lessons available

5. 5

   Vector Spaces

   Abstract vector spaces, subspaces, independence, bases and coordinates.

   4 topics · 4 lessons available

6. 6

   Vector Space Continued

   Dimension, rank, change of basis and discrete-time applications.

   4 topics · 4 lessons available

7. 7

   Eigenvalues and Eigen Vectors

   Eigenvalues, eigenvectors, diagonalization and dynamical systems.

   4 topics · 4 lessons available

8. 8

   Orthogonality and Least Squares

   Inner products, orthogonal sets, projections, QR factorization and least squares.

   4 topics · 4 lessons available

9. 9

   Groups and Subgroups

   Binary operations, group axioms, subgroups, cyclic groups and orders.

   4 topics · 4 lessons available

10. 10

    Rings and Fields

    Rings, integral domains, fields, subrings, ideals and homomorphisms.

    4 topics · 4 lessons available