This is a collection of interactive exercises which can be used to practice certain computational skills. A random exercise is created and you should then compute the solution. After hitting “update”, the solution will be shown so that you can compare with what you got. At the same time, a new exercise is created.
Foundations #
- Union, intersection, and set difference
- Power sets
- Injective, surjective, and bijective
- Fractions
- Complex numbers
- Division of polynomials
- Zeros of quadratic polynomials
Linear Algebra #
- Computations in finite fields
- Matrix multiplication
- Inverting matrices
- Determinants
- Characteristic polynomial
- Minimal polynomial
- Eigenvalues
- Diagonalizing matrices
- Jordan normal form
- Basis transformation
- Representing matrix
- Product of vectors
- Sylvester’s theorem
- Gram-Schmidt orthonormalization