Video Library
Essence of Linear Algebra
The four selections below build the geometric intuition that the written notes take for granted: what vectors and transformations are, what the determinant measures, and what column space means. The full series, together with interactive source material, is available from the author's website and YouTube channel.
Vectors — what even are they?
Essence of linear algebra · chapter 1Three perspectives on a vector — physics, computer science, mathematics — and why the abstraction is worth keeping all three in mind. A perfect companion to the first sections of the notes.
Linear transformations and matrices
Essence of linear algebra · chapter 3Why a matrix is best understood as a transformation of space, and why its columns are where the basis vectors land. Exactly the dictionary used by the transformation explorer demo.
The determinant
Essence of linear algebra · chapter 6The determinant as a signed area-scaling factor — and what a negative or zero determinant means geometrically. Try reproducing the examples with the sliders of the demo.
Inverse matrices, column space and null space
Essence of linear algebra · chapter 7Rank as dimensionality, column space as the image of the transformation, and null space as what gets crushed — the geometric core of solvability, connecting directly to the SVD notes.
How to use this shelf
- Watch chapters 1 and 3 before the SVD notes; the rotation–stretch–rotation picture will then feel inevitable.
- Chapter 6 pairs naturally with the determinant readout of the explorer demo.
- Chapter 7 is the best short preparation for the notions of rank and range used in the randomized approximation notes.