Click here for the notes

Well I compiled this by picking different bits from my revision notes then some careful fixes and some effort to make it smooth. The beginning two-third is a basic linear algebra course, and the last one-third is an advanced but interesting topic to cover: linear programming.

My general principle to arrange the contents is to solve three main problems: to compute the inverse of a matrix, the geometric implication of linear transformations, and the duality principle in linear programming. Some external guidance are also taken, like the classic

*Linear Algebra*from S. Lang.

Multiple references are taken, see p.3 of the text. I've taken [copied] some exercises from those references as well.

Ch.1 Basics: vector and matrix arithmetic

Ch,2 Linear system: reduction, independence, dimension

Ch.3 Geometry I: orthogonality, projection

Ch.4 Determinants: implication in lower dimensions, elementary matrices, matrix inverse, Cramer's rule

---

Ch.5 Abstract vector space: axioms, function space, inner product space

Ch.6 Linear Transformation: coordinate mapping, change of basis

Ch.7 Eigenvectors: diagonalization, applications

Ch.8 Special operators: Hermitian, unitary operators, orthogonal diagonalization, spectral decomposition

---

Ch.9 Geometry II: affine space, convex sets, cones

Ch.10 Polytopes and polyhedrons: V-H characterization, Fourier Motzkin elimination

Ch.11 Linear programming: Farkas Lemma, separation, simplex, duality

It was not the main motivation to get the old 1.5LA revamped, but actually I'm writing this for one of my dear friend who is studying computer science who is getting stuck with them, and I hope that there will be more readers other than him :)