Coding the Matrix: Linear Algebra through Computer Science Applications

When you take a digital photo with your phone or transform the image in Photoshop, when you play a video game or watch a movie with digital effects, when you do a web search or make a phone call, you are using technologies that build upon linear algebra.  Linear algebra provides concepts that are crucial to many areas of computer science, including graphics, image processing, cryptography, machine learning, computer vision, optimization, graph algorithms, quantum computation, computational biology, information retrieval and web search. Linear algebra in turn is built on two basic elements, the matrix and the vector.  
In this class, you will learn the concepts and methods of  linear algebra, and how to use them to think about problems arising in computer science.  You will write small programs in the programming language Python to  implement basic matrix and vector functionality and algorithms, and use these to process real-world data to achieve such tasks as: two-dimensional graphics transformations, face morphing, face detection, image transformations such as blurring and edge detection, image perspective removal, classification of tumors as malignant or  benign, integer factorization, error-correcting codes, and secret-sharing.

• The Function
• The Field
• The Vector
• The Vector Space
• The Matrix
• The Basis
• Dimension
• Gaussian Elimination
• The Inner Product
• Orthogonalization