Linear Algebra II: Matrices and Linear Transformations

Overview

What you'll learn

• Perform algebraic operations on matrices such as matrix multiplication and matrix inversion.
• Recognize linear transformations, apply their properties and find the standard matrix.
• Find the determinant of a matrix and apply properties of determinants in the context of algebra and geometry.
• Find eigenvalues, eigenvectors and eigenspaces of a matrix.
• Diagonalize a matrix if possible and perform other similarity transformations.
• Apply properties of symmetric matrices.
• Find the singular value decomposition of a matrix.

Syllabus 19

1. matrix multiplication and addition
2. matrix inversion
3. linear transformations
4. standard matrix of a linear transformation
5. examples of linear transformations in geometry
6. determinants
7. methods to find determinants
8. applications of determinants
9. eigenvalues and eigenvectors
10. eigenspaces
11. characteristic polynomials
12. complex eigenvalues
13. multiplicities of eigenvalues
14. diagonalization
15. similarity transformations
16. coordinate transformations
17. symmetric matrices
18. quadratic forms
19. singular value decomposition

Skills you'll practise

Quantum ComputingMathematicsLinear AlgebraMachine LearningEigenvalues And EigenvectorsBasic MathMatrix Algebra

Advantages and disadvantages

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Before you start

Prior knowledge of all the material covered. This is a self-contained bachelor-level course. However, we do assume that you are familiar with standard high school mathematics, specifically standard functions and their properties, algebraic manipulation of equations and inequalities and standard mathematical notation. This course is a review course. As such the course requires you to have studied linear algebra in the past or at least to be familiar with its course contents. If this is not the case for you, then you can still do the course, but be prepared for a high pace!

Taught by

• Bart van den DriesDr.
• Marleen KeijzerDr.
• Niek de KleijnPhD
• Willem Schouten-StraatmanDr.
• Iris SmitDr.
• Johannes MaksDr.