Topics Covered

Introduction

• Recall how machine learning and vectors and matrices are related
• Interpret how changes in the model parameters affect the quality of the fit to the training data
• Recognize that variations in the model parameters are vectors on the response surface - that vectors are a generic concept not limited to a physical real space
• Use substitution / elimination to solve a fairly easy linear algebra problem
• Understand how to add vectors and multiply by a scalar number

Vectors are objects that move around space

• Calculate basic operations (dot product, modulus, negation) on vectors
• Calculate a change of basis
• Recall linear independence
• Identify a linearly independent basis and relate this to the dimensionality of the space

Matrices in Linear Algebra: Objects that operate on Vectors

• Understand what a matrix is and how it corresponds to a transformation.
• Explain and calculate inverse and determinant of matrices
• Identify and explain how to find inverses computationally and what goes wrong.

Matrices Make Linear Mappings

• Identify matrices as operators
• Relate the transformation matrix to a set of new basis vectors
• Formulate code for mappings based on these transformation matrices
• Write code to find an orthonormal basis set computationally

Eigen Value and Eigenvectors

• Identify geometrically what an eigenvector/value is
• Apply mathematical formulation in simple cases
• Build an intuition of larger dimention eigensystems
• Write code to solve a large dimentional eigen problem