# Linear Algebra, Semester 2, 2016

Office hours: Mon 1:00 - 2:15, Wed 1:00 - 2:15, Fri 1:00-1:30 Richard Berry 169

## Supplementary slides

 Slides Summary Systems of linear equations Pictures and ways to think about systems of linear equations in two variables Lengths and Angles Length, angles, projections and the Cauchy-Schwarz inequality Linear Transformations Addition and linear transformations in Euclidean space Matrix Multiplication and Inverses Matrix multiplication from a number of different perspectives. Bases and Dimension Linear independence, spanning sets, bases and dimension. Determinants Volume and determinants Areas of triangles Areas of parallelograms and triangles Planes and lines A summary of the different ways to describe planes and lines in three dimensional euclidean space and how to switch between them How was the cross product organized in the lecture? p.84 definition of cross product, p.91 "scalar triple product" satisfies determinant axioms, p.87 geometric applications, proved by the slide titled "In 3 dimensions" in "Areas of Triangles", p.83 Example, p.85 Algebraic properties of the cross product, p.86 Geometry of the cross product: the formula with sin is deduced from area(P)=|u| height(P) = |u| |v| sin(theta) and from p.87 Special Relativity (elementary version) Special relativity theory explained at highschool level, no knowledge of matrices required Fast Integer Multiplication The fastFourire Transforma nd the Schoenhage Strassen Algorithm Special Relativity (advanced) Special relativity revisited, incorporating some of the more advanced concepts of the course Can you hear the shape of a drum? A talk I once gave on the spectral theorem Rank Nullity Theorem Singular Value Decomposition Open Key Encryption An old MUMS talk The (8,4)-Hamming Code Error correcting codes following Hamming

## Links of interest to the course

Some applications of Linear Algebra

On the electrodynamics of moving bodies by Albert Einstein, June 30, 1905 (English translation).

Molecular vibration If you are interested in applications to Chemistry, you might enjoy the last chapter of this book by James and Liebeck

Jordan Ellenberg's Linear Algebra notes (2000)

Jim Hefferson's text Thanks to Tom from the 2013 class for this link to a text with many worked examples.

#### Linear Algebra through computer science applications

Thanks to Mostafa from the 2013 class and Alex Ghitza for pointing out these links:

Machine learning with Python Tutorial about implementing a linear regression algorithm, the emphasis is on computer science rather than linear algebra.

Machine Learning MOOC An online course about Machine Learning that heavily uses matrices and linear algebra.

Applications of Linear Algebra to Computer Science MOOC Another open online course, exploring various applications of linear algebra to computer science.