ROB-GY 6013 · Mathematics for Robotics · Fall 2026
Version 1 · 2026-10-04
Lectures are self-contained: you do not need to buy anything to follow them. This page exists so you can tell where a definition comes from, what to read if you want more, and — when a book writes something differently — which difference is a convention and which is a different statement.
Reading is optional; nothing here is an assignment, and no book has to be bought. Four of them are free to read online from the publisher or author — Goodfellow, Bengio and Courville; Axler's fourth edition; Lynch and Park; Boyd and Vandenberghe — and each is linked below. The others are ordinary library books.
Five different kinds of thing get cited on a references page, and they carry different authority.
| category | what it is good for | what it is not |
|---|---|---|
| Textbook | definitions, statements, proofs you can cite | not necessarily our notation |
| Course notes | a second explanation, often closer to our level | not peer-reviewed; conventions vary by course |
| Survey or tutorial | a map of a field, or a derivation worked in detail | not a textbook; coverage is deliberately partial |
| Visual explanation | intuition, the picture behind a formula | not where to check a shape, a hypothesis or a sign |
| Coding practice | somewhere to implement and be graded | never the mathematical or notational authority |
Linear algebra, Lectures 1–4 — Gilbert Strang, Linear Algebra and Learning from Data, Wellesley–Cambridge Press, 2019. Written for exactly this audience: matrices, subspaces, factorizations and learning in one book. Its chapter order is not our lecture order.
Networks and backpropagation, Lecture 5 — Goodfellow, Bengio and Courville, Deep Learning, MIT Press, 2016, free online. Chapter 6, Deep Feedforward Networks, is the chapter for Lecture 5; §6.5, Back-Propagation and Other Differentiation Algorithms, is the section. Chapters 2 (Linear Algebra) and 4 (Numerical Computation) are the background.
Definitions and proofs — Sheldon Axler, Linear Algebra Done Right, 4th edition, Springer, 2024, open access. The place to go when you want a statement proved properly. It is deliberately abstract, so it will not teach you this course's computational conventions.
Robotics — Lynch and Park, Modern Robotics: Mechanics, Planning, and Control, Cambridge, 2017, free online. For robot Jacobians, singularities and inverse kinematics. Note that its spatial and body Jacobians stack angular with linear velocity; the position-only Jacobian we use is a smaller object.
Also cited where actually used — Boyd and Vandenberghe, Introduction to Applied Linear Algebra, Cambridge, 2018, free online; Trefethen and Bau, Numerical Linear Algebra, SIAM, 1997, for numerical QR, SVD and conditioning; Horn and Johnson, Matrix Analysis, 2nd ed., Cambridge, 2012.
| lecture | primary reading | supplement | notation difference |
|---|---|---|---|
| 1 spaces, rank, four subspaces |
Strang, Learning from Data, Part I | Axler, ch. 1–3; Deep Learning ch. 2 | Strang writes $\mathcal C(A)$ and $\mathcal N(A)$, and so does this lecture; Lectures 3 to 5 display $\operatorname{Col}(A)$ and $\operatorname{Null}(A)$. The notation page carries the mapping |
| 2 eigenvalues, symmetry, quadratic forms |
Axler, ch. 5 and 7 | Deep Learning §2.7–2.8; Horn & Johnson for the Jordan form | Axler works over $\mathbb C$ and proves existence differently; this lecture works over $\mathbb R$, and states separately which results need symmetry |
| 3 orthogonality, projection, least squares |
Axler §6A–6C | Trefethen & Bau; Boyd & Vandenberghe | books differ on whether the loss carries a $\tfrac12$; ours is stated on each page |
| 4 PSD, SVD, PCA, pseudoinverse |
Strang, Learning from Data | Deep Learning §2.7–2.9, §2.12, §4.2–4.3; Trefethen & Bau | data dimensions are $N$ samples by $d$ features here, $B$ by $n$ in Lecture 5 — same arrangement, different letters |
| 5 matrix calculus and backpropagation |
Deep Learning ch. 6, especially §6.5 | Parr & Howard for worked matrix calculus; Baydin et al. for automatic differentiation; CS231n for a second explanation | sources differ on row versus column gradients and on batch layout; see the notation page |
Provenance of the section numbers above
The Deep Learning sections were checked against the book's own table of contents on 2026-10-04: ch. 2 Linear Algebra (2.7 Eigendecomposition, 2.8 Singular Value Decomposition, 2.9 The Moore-Penrose Pseudoinverse, 2.12 Example: Principal Components Analysis), ch. 4 Numerical Computation (4.2 Poor Conditioning, 4.3 Gradient-Based Optimization), ch. 6 Deep Feedforward Networks (6.5 Back-Propagation and Other Differentiation Algorithms). The Strang, Axler, Trefethen & Bau, Boyd & Vandenberghe and Modern Robotics pointers are carried over from the lecture reference pages where they were first cited, and are given at chapter or part level here rather than restated more precisely than they were verified.
| source | category | used for |
|---|---|---|
| Strang, MIT 18.06, OCW 2010 | Course notes / lectures | a second explanation of the linear algebra core. The video course and the 2019 book are different items by the same author. |
| Grizzle, ROB 501, Michigan | Course notes | robotics-facing linear algebra and least squares |
| Stanford CS231n notes | Course notes | backpropagation intuition, and gradient checking |
| Baydin, Pearlmutter, Radul & Siskind, JMLR 2018 | Survey | what automatic differentiation is, and what it is not |
| Parr & Howard, arXiv:1802.01528 | Tutorial | matrix calculus worked in detail |
| Buss, Introduction to Inverse Kinematics, UCSD 2004 | Tutorial | damped least squares for inverse kinematics |
| 3Blue1Brown, Essence of Linear Algebra | Visual explanation | intuition before the algebra |
| TorchCode (duoan/TorchCode, MIT licence) | Coding practice | auto-graded by-hand tensor exercises. A practice resource, not a source of notation. |
| Research papers cited in individual lectures | Research | where a method came from; not written for a first reading |
Lecture notes follow the course's own Notation and Conventions. The main linear-algebra reference is Strang's Linear Algebra and Learning from Data (2019); the main neural-network and backpropagation reference is Goodfellow, Bengio and Courville's Deep Learning (2016). Axler and Modern Robotics are the mathematical and robotics supplements. Where a reading is suggested, the lecture names the section and any notation difference.
No book is required. The Deep Learning book, Axler's fourth edition, Modern Robotics and Boyd & Vandenberghe are free to read from the publisher or author; Strang, Trefethen & Bau and Horn & Johnson are library books.