Spaces, maps, bases, eigenvectors, diagonalization.
Course Module
Linear algebra and differential equations belong together.
MATH 5520H is not just a list of techniques. The point of this page is to connect vector spaces, eigenvalues, diagonalization, systems of differential equations, stability, and matrix exponentials so the course feels like one structure.
Use matrices to describe coupled change.
Solve and classify x' = Ax using algebraic information.
Movable Concept Map
Drag the concepts while studying relationships.
Click a node to read what it contributes to the course.
Selected Concept
Vector Spaces
A vector space gives the setting where linear combinations, bases, dimension, and coordinate representations make sense.
- Ask: what objects are the vectors?
- Track: basis, dimension, subspace, span, independence.
Linear System Lab
Classify x' = Ax from trace and determinant.
Move the matrix entries and watch the phase portrait update. This is the algebra-to-ODE bridge: eigenvalues control stability.
- Matrix A
- [1, -2; 2, -1]
- Trace
- 0
- Determinant
- 3
- Classification
- Center or spiral boundary
Course Notes
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