Linear algebra tutoring for university students
Linear algebra is often the first course where you have to prove instead of calculate. I work through the material with you until you see why a theorem holds, not just how to do the exercise.
What we work through
Systems and matrices
- Gaussian elimination
- Rank, kernel and image
- Rank-nullity theorem
Determinants and inverse
- Rules and computation
- Invertibility
- The link with area and volume
Eigenvalues and diagonalisation
- Eigenvalues and eigenspaces
- Diagonalisability
- Applications to sequences and dynamical systems
Vector spaces and orthogonality
- Basis, dimension, linear maps
- Inner product and Gram-Schmidt
- Least squares and the spectral theorem
Which courses?
- UvA BSc Mathematics, e.g. a first-year Linear Algebra course
- UvA BSc Econometrics & Data Science, e.g. Linear Algebra
- UvA BSc Actuarial Science, e.g. a maths course with matrix algebra
- VU BSc Econometrics & Operations Research, e.g. Linear Algebra
- VU BSc Mathematics, e.g. Linear Algebra
These are examples (e.g.). Course names and content change from year to year, so check your own study guide. Send me your course and I will look at what you need.
Where it often goes wrong
det(A+B) ≠ det A + det B
The determinant is multiplicative: det(AB) = det A · det B. It does not work for sums, and two 2×2 matrices already show it.
An eigenvector is not unique
Every nonzero multiple of an eigenvector is an eigenvector too. Exams therefore often ask for a basis of the eigenspace, not for "the" eigenvector.
AB ≠ BA
Matrix multiplication is not commutative. Many wrong derivations start by quietly swapping the order.
What does it cost?
- With a tutor from our team (student tutor) from €250 per 4-hour package, 1 student.
- With me personally €300 online or €400 on location per 4-hour package, 1 student.
Two or more students can pay less per person, see the price table on the contact page.
Want to see if I can help?
Send me a message with your course and when your exam is. I reply myself.