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, […]

# Archive | Linear Algebra

## 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 […]

## 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 […]

## Gentle Introduction to Vector Norms in Machine Learning

Calculating the length or magnitude of vectors is often required either directly as a regularization method in machine learning, or as part of broader vector or matrix operations. In this tutorial, you will discover the different ways to calculate vector lengths or magnitudes, called the vector norm. After completing this tutorial, you will know: The […]

## A Gentle Introduction to Vectors for Machine Learning

Vectors are a foundational element of linear algebra. Vectors are used throughout the field of machine learning in the description of algorithms and processes such as the target variable (y) when training an algorithm. In this tutorial, you will discover linear algebra vectors for machine learning. After completing this tutorial, you will know: What a […]

## A Gentle Introduction to NumPy Arrays in Python

Arrays are the main data structure used in machine learning. In Python, arrays from the NumPy library, called N-dimensional arrays or the ndarray, are used as the primary data structure for representing data. In this tutorial, you will discover the N-dimensional array in NumPy for representing numerical and manipulating data in Python. After completing this […]

## 5 Reasons to Learn Linear Algebra for Machine Learning

Why Learn Linear Algebra for Machine Learning? Linear algebra is a field of mathematics that could be called the mathematics of data. It is undeniably a pillar of the field of machine learning, and many recommend it as a prerequisite subject to study prior to getting started in machine learning. This is misleading advice, as […]