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