# Syllabus

## Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session

## Prerequisites

Multivariable Calculus (18.02)

## Text

The readings are assigned in:  Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714.

Reading assignments are also provided for the newer edition: Introduction to Linear Algebra. 5th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2016. ISBN: 9780980232776.

NOTE: More material on linear algebra (and much more about differential equations) is in Professor Strang's 2014 textbook Differential Equations and Linear Algebra. In 2016, the textbook was developed into a series of 55 short videos, Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler.

## Goals

The goals for 18.06 are using matrices and also understanding them.

Here are key computations and some of the ideas behind them:

1. Solving Ax = b for square systems by elimination (pivots, multipliers, back substitution, invertibility of A, factorization into A = LU)
2. Complete solution to Ax = b (column space containing b, rank of A, nullspace of A and special solutions to Ax = 0 from row reduced R)
3. Basis and dimension (bases for the four fundamental subspaces)
4. Least squares solutions (closest line by understanding projections)
5. Orthogonalization by Gram-Schmidt (factorization into A = QR)
6. Properties of determinants (leading to the cofactor formula and the sum over all n! permutations, applications to inv(A) and volume)
7. Eigenvalues and eigenvectors (diagonalizing A, computing powers A^k and matrix exponentials to solve difference and differential equations)
8. Symmetric matrices and positive definite matrices (real eigenvalues and orthogonal eigenvectors, tests for x'Ax > 0, applications)
9. Linear transformations and change of basis (connected to the Singular Value Decomposition - orthonormal bases that diagonalize A)
10. Linear algebra in engineering (graphs and networks, Markov matrices, Fourier matrix, Fast Fourier Transform, linear programming)

## Homework

The homeworks are essential in learning linear algebra. They are not a test and you are encouraged to talk to other students about difficult problems-after you have found them difficult. Talking about linear algebra is healthy. But you must write your own solutions.

## Exams

There will be three one-hour exams at class times and a final exam. The use of calculators or notes is not permitted during the exams.