# Archive | Linear Algebra ## A Gentle Introduction to Expected Value, Variance, and Covariance with NumPy

Fundamental statistics are useful tools in applied machine learning for a better understanding your data. They are also the tools that provide the foundation for more advanced linear algebra operations and machine learning methods, such as the covariance matrix and principal component analysis respectively. As such, it is important to have a strong grip on […] ## How to Calculate the SVD from Scratch with Python

Matrix decomposition, also known as matrix factorization, involves describing a given matrix using its constituent elements. Perhaps the most known and widely used matrix decomposition method is the Singular-Value Decomposition, or SVD. All matrices have an SVD, which makes it more stable than other methods, such as the eigendecomposition. As such, it is often used […] ## Linear Algebra Cheat Sheet for Machine Learning

All of the Linear Algebra Operations that You Need to Use in NumPy for Machine Learning. The Python numerical computation library called NumPy provides many linear algebra functions that may be useful as a machine learning practitioner. In this tutorial, you will discover the key functions for working with vectors and matrices that you may […] ## Top Resources for Learning Linear Algebra for Machine Learning

How to Get Help with Linear Algebra for Machine Learning? Linear algebra is a field of mathematics and an important pillar of the field of machine learning. It can be a challenging topic for beginners, or for practitioners who have not looked at the topic in decades. In this post, you will discover how to […] ## Gentle Introduction to Eigenvalues and Eigenvectors for Machine Learning

Matrix decompositions are a useful tool for reducing a matrix to their constituent parts in order to simplify a range of more complex operations. Perhaps the most used type of matrix decomposition is the eigendecomposition that decomposes a matrix into eigenvectors and eigenvalues. This decomposition also plays a role in methods used in machine learning, […] ## A Gentle Introduction to Matrix Factorization for Machine Learning

Many complex matrix operations cannot be solved efficiently or with stability using the limited precision of computers. Matrix decompositions are methods that reduce a matrix into constituent parts that make it easier to calculate more complex matrix operations. Matrix decomposition methods, also called matrix factorization methods, are a foundation of linear algebra in computers, even […] ## A Gentle Introduction to Tensors for Machine Learning with NumPy

In deep learning it is common to see a lot of discussion around tensors as the cornerstone data structure. Tensor even appears in name of Google’s flagship machine learning library: “TensorFlow“. Tensors are a type of data structure used in linear algebra, and like vectors and matrices, you can calculate arithmetic operations with tensors. In […] ## A Gentle Introduction to Matrix Operations for Machine Learning

Matrix operations are used in the description of many machine learning algorithms. Some operations can be used directly to solve key equations, whereas others provide useful shorthand or foundation in the description and the use of more complex matrix operations. In this tutorial, you will discover important linear algebra matrix operations used in the description […] ## Introduction to Matrix Types in Linear Algebra for Machine Learning

A lot of linear algebra is concerned with operations on vectors and matrices, and there are many different types of matrices. There are a few types of matrices that you may encounter again and again when getting started in linear algebra, particularity the parts of linear algebra relevant to machine learning. In this tutorial, you […] ## Introduction to Matrices and Matrix Arithmetic for Machine Learning

Matrices are a foundational element of linear algebra. Matrices are used throughout the field of machine learning in the description of algorithms and processes such as the input data variable (X) when training an algorithm. In this tutorial, you will discover matrices in linear algebra and how to manipulate them in Python. After completing this […]