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Lecture notes for Math 115A (linear algebra) - mklabgr - 07-16-2026
Lecture notes for Math 115A (linear algebra)
by Terence Tao
Summary
This document contains Terence Tao’s comprehensive undergraduate lecture notes for Math 115A, an introductory course in linear algebra taught at UCLA in Fall 2002, which closely aligns with the Friedberg, Insel, and Spence textbook. Rather than focusing purely on computational mechanics, these notes emphasize the foundational theory, conceptual definitions, and rigorous mathematical proofs behind linear systems.
The curriculum is systematically structured into a multi-week progression: the first two weeks establish the foundational rules of vector spaces, subspaces, linear independence, spans, bases, and dimensions; weeks three through five examine the algebraic properties of linear transformations and their coordinate representations; weeks six through eight shift the focus to matrix analysis, introducing tools such as determinants, eigenvectors, eigenvalues, trace, and diagonalization to simplify and visualize complex transformations; and the final weeks introduce inner product spaces, which extend vector spaces to include geometric concepts like lengths, angles, and orthogonality. Ultimately, Tao frames linear algebra as the study of linear transformations, illustrating how multidimensional systems can be elegantly decomposed and solved through systematic algebraic frameworks.
NOTES [PDF]