*Introductory*

- Introduction to linear transformations
- Linear sums and independence, span, and linear bases
- Why matrices?
- Composition of linear transformations: matrix multiplication
- Inverses, determinants, column spaces, non-square matrices
- Null and row spaces, transpose and the dot product
- Basis changes
- What does it mean for two matrices to commute?
- Eigen-everything, diagonalisation, repeated eigenvalues
- Generalised eigenvectors, Jordan normal form
- An introduction to forms

*More*

- Trace and its links to determinant and eigenvalues
- Some interesting theorems in linear algebra
- Complex linear algebra
- The Hilbert space
- Some matrix theory
- Affine transformations

*Insight into cross products series*

- Quaternions introduction: Part I
- Quarternions introduction: Part II
- Octonions and beyond
- Exterior products (aka: a primer on tensors)
- That silly formal determinant

*Reference*

- Computational techniques (proofs regarding direct formulae for determinants, inverses)
- The geometry of $\mathbb{R}^n$ -- cross product, planes, projections, 3D rotations, etc.

*Resources*

- The Essence of Linear Algebra youtube video series (3Blue1Brown) [
*insight*] - Khan Academy Linear Algebra [
*companion*] - Schaum's outlines: linear algebra [
*companion*] - Calculus II (Apostol) -- chapters 1-5 [
*companion*] - Linear Algebra done right (Axler) [
*textbook*] - Linear Algebra done wrong (Treil) [
*textbook*] - Introduction to linear algebra (Lang) [
*textbook*] - A primer on linear algebra (Herstein) [
*textbook*] - Introduction to Linear Algebra (Strang) [
*textbook*] - Linear Algebra (Lang) [
*textbook2*] - Matrix theory and linear algebra (Herstein) [
*textbook2*] - Linear Algebra and its applications (Lax) [
*textbook2*] - Linear Algebra and its applications (Strang) [
*textbook2*]

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