Linear Algebra I
M04 — Fall 25
Contents
1 Fields and complex numbers
1.1 Fields
1.2 Complex numbers
2 Matrices
2.1 Definitions
2.2 Matrix operations
2.3 Mappings associated to matrices
3 Vector spaces and linear maps
3.1 Vector spaces
3.2 Linear maps
3.3 Vector subspaces and isomorphisms
3.4 Generating sets
3.5 Linear independence and bases
3.6 The dimension
3.7 Matrix representation of linear maps
4 Applications of Gaussian elimination
4.1 Gaussian elimination
4.2 Applications
5 The determinant
5.1 Axiomatic characterisation
5.2 Uniqueness of the determinant
5.3 Existence of the determinant
5.4 Properties of the determinant
5.5 Permutations
5.6 The Leibniz formula
5.7 Cramer’s rule
6 Endomorphisms
6.1 Sums, direct sums and complements
6.2 Invariants of endomorphisms
6.3 Eigenvectors and eigenvalues
6.4 The characteristic polynomial
6.5 Properties of eigenvalues
6.6 Special endomorphisms
7 Quotient vector spaces
7.1 Affine mappings and affine spaces
7.2 Quotient vector spaces
Linear Algebra I
Home
Contents
Exercises
Lecture Recordings
Quizzes
Study Weeks
✕