MATH0005 Algebra 1
About these notes
1
Logic
2
Sets and functions
3
Matrices
4
Linear algebra
4.1
Fields
4.2
Vector spaces
4.3
Using the vector space axioms
4.4
Subspaces
4.5
Sums and intersections
4.6
Linear independence
4.7
Spanning sequences
4.8
Bases
4.9
Dimension
4.10
Basis and dimension examples
4.11
Fundamental solutions are linearly independent
4.12
Extending to a basis
4.13
Finding dimensions
4.14
Linear maps
4.15
Kernel and image
4.16
The rank-nullity theorem
4.17
Matrix nullspace basis
4.18
Column space basis
4.19
Matrix of a linear map
4.20
Matrix of a composition
4.21
Change of basis
Further reading
MATH0005 Algebra 1
Further reading
4.1
Fields
Chapter 4
Linear algebra
4.1
Fields
4.2
Vector spaces
4.3
Using the vector space axioms
4.4
Subspaces
4.5
Sums and intersections
4.6
Linear independence
4.7
Spanning sequences
4.8
Bases
4.9
Dimension
4.10
Basis and dimension examples
4.11
Fundamental solutions are linearly independent
4.12
Extending to a basis
4.13
Finding dimensions
4.14
Linear maps
4.15
Kernel and image
4.16
The rank-nullity theorem
4.17
Matrix nullspace basis
4.18
Column space basis
4.19
Matrix of a linear map
4.20
Matrix of a composition
4.21
Change of basis
Further reading