Lecture notes · MATH241 · 11 sections
Linear Algebra
A complete set of lecture notes, typed up from the handwritten originals with every mistake fixed. They run from complex numbers through linear algebra to transforms and differential equations, with the same few ideas underneath.
The sections
Each section keeps every line of the original notes, in order, and can be read online or taken away as a PDF or as LaTeX.
1Complex NumbersReal and imaginary parts, complex arithmetic, conjugates and modulus, the triangle inequality, Euler's formula and the polar form.
- Algebra of complex numbers
- Conjugate and modulus
- Triangle inequality
- Euler's formula
- Gauss elimination
- Gauss–Jordan and pivoting
- Vector spaces
- Norms and dot products
- Span and subspaces
- Linear independence
- Basis and dimension
- Projection and Gram–Schmidt
- Matrix operations
- Determinants
- Rank and null space
- Inverses and LU
- Eigenpairs
- Symmetric matrices
- Diagonalization
- Cayley–Hamilton and e^(At)
- Singular values
- Singular vectors
- Scaling picture
- Rank-one expansion
- Canonical form
- Definiteness
- Curve fitting
- Normal equations
- Matrix form
- Eigenvector solution
- Characteristic roots
- Repeated roots
- Z-transform
- Solving difference equations
- Differential equations
- Stability and oscillators
- Definition and existence
- Properties
- Convolution
- Solving differential equations
- Systems and Laplace
- State-transition matrix
- Variation of parameters
- Time-varying systems
Notation
The handwritten notes mark the type of an object by underlining it. Here the usual textbook convention is used instead.
| Object | In the handwritten notes | On these pages |
|---|---|---|
| Scalar (a number) | plain, a | italic, a, α, c |
| Complex number | underlined once, z | italic, z (it is a scalar) |
| Vector | underlined once, u | bold, u |
| Matrix | underlined twice, A | italic capital, A (zero matrix O, identity I) |
So the equation written Ax = c in the notes appears here as Ax = c.
Take it with you
The whole corrected set as one PDF. Every section also has its own PDF and a zip with the LaTeX source, so you can take out just the part you need.