Math 1b Analytic is a course on linear algebra over the real and complex numbers, emphasizing the theoretical (as opposed to the computational) aspects of the subject.

Course Policies

For the policies on grading and homework, please consult the official course page. Please note that you are allowed a single one-week homework extension during the quarter. If you would like to use this extension, please email me at least 24 hours before the homework is due.

You can attend my recitations, office hours, or send me emails even if you are not officially registered for my sections.

Textbooks

We use "Apostol II" (Apostol's Calculus, Volume 2) as the course textbook. It is a good reference book, and is one of the few textbooks that really ties together single-variable calculus, linear algebra, and multivariable calculus into a unified thread; this is unsurprising, since the book was specifically developed for the Caltech Ma 1abc series.

Announcements

• The first session will take place on January 8th.

Recitation Notes

• Session 1 (01/08): Course philosophy, vector spaces, subspaces, polynomials.
• Session 2 (01/15): Linear independence, bases, dimension, linear transformations, rank, and nullity.
• Session 3 (01/22): injective/surjective/bijective maps, matrix representations, change of bases, invariants of linear maps.
• Session 4 (01/29): Theory behind row reduction and inverse algorithms, systems of linear equations, invertible matrices, similarity.
• Session 5 (02/05): Midterm review.
• Session 6 (02/12): Determinants, Cramer's rule, matrix minors.
• Session 7 (02/19): Eigenvectors and eigenvalues.
• Session 8 (02/26): Inner product spaces, norms, orthogonality, Gram-Schmidt process, orthogonal projections.
• Session 9 (03/05): Linear algebra from 10,000 feet; orthogonal, unitary, hermitian, skew-hermitian matrices; complex spectral theorem.

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