16-706 Robotic Foundations: Algebra
6 units, Carnegie Mellon University
Linear algebra underlies nearly every area of robotics, including perception, control, planning, estimation, and learning. In fact, many failures in modern robotic systems arise not from missing algorithms, but from misunderstandings of representation, geometry, conditioning, and observability. This PhD-level mini course rebuilds a geometric and inferential understanding of linear algebra as it appears implicitly inside modern robotic systems. Rather than emphasizing formula memorization or procedural computation, the course treats linear algebra as a diagnostic language for reasoning about what a system can represent, what information is preserved or lost, when ambiguity is structural rather than statistical, and why certain failures occur silently rather than catastrophically. The course follows a deliberate arc: (1) Representation and Geometry, (2) Inference and Stability, and (3) Degeneracy and Observability. Students revisit vectors, linear transformations, rank, least squares, eigenvalues, singular values, conditioning and projective geometry through formal definitions, geometric intuition, and modern robotics framing. This course is not a first introduction to linear algebra and is not programming-heavy. It is a compact, concept-driven reset intended to strengthen research-level reasoning in robotics.
Prerequisites: none listed
Offered: Fall 2026
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