MathIsimple
Part III

Linear Mappings

Linear maps are structure-preserving functions between vector spaces. They are the morphisms in the category of vector spaces—the heart of linear algebra.

5
Courses
12-17
Hours
Core
Level

Courses

LA-3.1
Linear Map Definition
Available
Definition, examples, and basic properties of linear maps
3-4 hours
Definition
Examples
Composition
Space of Linear Maps
LA-3.2
Kernel & Image
Available
Null space and range of linear maps
2-3 hours
Kernel
Image
Injectivity
Surjectivity
LA-3.3
Rank-Nullity Theorem
Available
The fundamental dimension formula for linear maps
2-3 hours
Statement
Proof
Applications
Consequences
LA-3.4
Isomorphisms
Available
Bijective linear maps and structure preservation
2-3 hours
Definition
Characterization
V ≅ Fⁿ
Isomorphism Classes
LA-3.5
Dual Spaces
Available
Linear functionals, dual basis, and double dual
3-4 hours
Linear Functionals
Dual Space V*
Dual Basis
Annihilators