**Course Description:** AM 10 provides an introduction to linear algebra and its applications. In addition, students will learn to use computational software (MATLAB/OCTAVE) and the basics of numerical linear algebra.

**Instructor: **Prof. Daniele Venturi (venturi@ucsc.edu)

Teaching Assistants:

- Long Lu, lklu@ucsc.edu
- Joseph Moore, jonimoor@ucsc.edu
- Poonam Deshpande, podeshpa@ucsc.edu
- Shashank Gandhi, shgandhi@ucsc.edu

Main Lectures: Tu/Th 9:50AM-11:25AM, (Remote instruction)

Section: Wednesday 5:20PM-6:55PM Jack Baskin Auditorium (BE-101)

**CANVAS COURSE WEBPAGE: CANVAS**

**LECTURE NOTES: PDF**

Group tutoring section: Friday 4:00PM-5:05PM (Remote instruction) held by Long Lu

**Office Hours: **

- Daniele Venturi (remote), Wednesday 11AM-12PM
- Joseph Moore BE 312 C/D (in person), Friday 2PM-4PM
- Poonam Deshpande, BE 312 C/D (in person), Thursday 3:30PM-5:30PM
- Shashank Gandhi BE 312 C/D (in person), Monday 11:30AM-1:30PM

Homework Assignments, Grading Policy and Exams: See CANVAS course webpage.

**Course Syllabus: **

*Week 1:*Real numbers and introduction to complex numbers*Week 2:*Complex numbers, algebraic and polar form, De Moivre formula, complex exponential function, nth root of a complex number, quadratic quations and polynomial equations in the complex plane.*Week 3:*Homogeneous linear equations, matrices, row operations and Gauss elimination, linear combination.*Week 4:*Matrix algebra, multiplication and addition, matrices associated with linear systems, LU factorization.*Week 5:*Vector spaces, linear combinations, linear independendence, dimension, matrix rank.*Week 6:*Linear Maps, kernel and image of a linear map, matrix associated with a linear map, change of bases.*Week 7:*Scalar products, orthogonal bases, bilinear maps and matrices.*Week 8:*Determinants, Cramer's rule, inverse of a matrix.*Week 9:*Eigenvalues and eigenvectors, characteristic polynomial, geometric and algebraic multiplicity of eigenvalues.*Week 10: S*imilarity transformations, diagonalization.

**Textbooks:**

- Serge Lang, ``Introduction to linear algebra'', Springer

https://link.springer.com/

- Thomas Shores, ``Applied Linear Algebra and Matrix Analysis'', Springer

https://link.springer.com/book/10.1007/978-3-319-74748-4 (free download from campus network)

- Serge Lang, ``Llinear algebra'', Springer

https://link.springer.com/book/10.1007/978-1-4757-1949-9 (free download from campus network)