- Determine and prove properties of functions (well-definedness, injectivity, surjectivity, linearity);
- Prove that a relation is an equivalence relation;
- Know some examples for groups, rings, and fields;
- Solve linear systems, multiply and invert matrices;
- Test vectors for linear (in)dependence;
- Understand classical proofs of theorems about vector spaces;
- Prove elementary facts in the theory of vector spaces independently;
- Perform vector space operations (sum, intersection, quotient, basis change, dimension computation, etc.)
- Interpret vector space notions and operations geometrically
|
Notion of function, relations, algebraic structures, matrix calculus, theorems and proofs of the theory of vector spaces (e.g. dimension theorems and homomorphism theorem)
|
