This short lesson summarizes the topics we covered in section 13 and why they'll be important to you as a data scientist.
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
The goal of section 13 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 dimsional 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 additiona 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 imstead to solve a linear regression