Linear Algebra
MATH1900: Machine Learning
Location: http://people.sc.fsu.edu/∼jburkardt/classes/ml 2019/linear algebra/linear algebra.pdf
Matrices and vectors describe simple linear transformations
Machine learning looks for patterns and structures in data. Linear relationships are often the best simple
approximation to complicated systems. Linear algebra is a collection of ideas and tools that we can use to
construct these simple models of our observations.
In linear algebra, we study abstract objects called vectors; in machine learning, these are the individual
observations of temperature, answers on a survey, medical records. While in machine learning, we might
have a table whose rows are the observations, linear algebra thinks of this as a matrix. Linear algebra can
help us decide whether
• two observations are very similar;
• your hospital bill can be approximately predicted by your sex, age, and smoking status;
• an image we have scanned is a picture of a cat or a dog.
The Linear Algebra Problem
How can we use the tools of linear algebra to analyze our data when we think of it as vectors? In
particular, we want to:
• initialize a vector;
• compute the norm (size) of a vector;
• compute the distance and angle between two vectors;
• initialize a matrix;
• multiply a vector by a matrix;
• solve a system of linear equations;
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