allankim-learnco / dsc-linalg-section-recap-dc-ds-060319

Section 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.

Objectives

You will be able to:

• Understand and explain what was covered in this section
• Understand and explain why this section will help you become a data scientist

Key Takeaways

The goal of section 26 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:

• Understanding Linear Algebra will provide you a much stronger foundation when learning a range of data science topics - from Support Vector Machines and deep learning through Natural Language Processing and dimensionality reduction techniques like Principle Component Analysis
• 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
• Broadcasting allows for the addition of matrices of different shapes by extending the dimensions of the smaller matrix to match the dimensions of the larger one
• To calculate the dot product for matrix multiplication, the first matrix must have the same number of columns and the second has rows.
• Matrix multiplication is distributive and associative, but not commutative
• 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