dsc-linalg-section-recap-chicago-ds-102819's Introduction

Linear Algebra - Recap

Introduction

In this section, you learned the fundamentals of linear algebra. An understanding of linear algebra will help you better understand the underlying mathematics behind some machine learning algorithms.

Key Takeaways

The goal of this section was to provide both a conceptual and computational introduction to linear algebra - one of the foundational concepts underlying most machine learning models. Some of the key takeaways include:

One use case for vectors and matrices is for representing and solving systems of linear equations
A scalar is a single, real number. A vector is a one-dimensional array of numbers. A matrix is a 2-dimensional array of numbers
A tensor is a generalized term for an n-dimensional rectangular grid of numbers. A vector is a one-dimensional (first-order tensor), a matrix is a two-dimensional (second-order tensor), etc.
Two matrices can be added together if they have the same shape
Scalars can be added to matrices by adding the scalar (number) to each element
To calculate the dot product for matrix multiplication, the first matrix must have the same number of columns as the number of rows in the second matrix
Operating on NumPy data types is substantially more computationally efficient than performing the same operations on native Python data types
It is possible to use linear algebra in NumPy to solve for a linear regression using the OLS method
OLS is not computationally efficient, so in practice, we usually perform a gradient descent instead to solve a linear regression

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