Last Updated on August 9, 2019 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 L1 norm that is calculated as the sum of the absolute values of the vector. The L2 norm that […]

Last Updated on August 9, 2019 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 tutorial, you will know: What a matrix is and how to define one in Python with NumPy. How to […]

Last Updated on August 9, 2019 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 will discover a suite of different types of matrices from the field of linear algebra that you may encounter […]

Last Updated on August 9, 2019 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 of machine learning methods. After completing this tutorial, you will know: The Transpose operation for flipping the dimensions of […]

Last Updated on December 6, 2019 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 this tutorial, you will discover what tensors are and how to manipulate them in Python with NumPy After completing […]

Last Updated on August 9, 2019 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 for basic operations such as solving systems of linear equations, calculating the inverse, and calculating the determinant of a […]

Last Updated on August 9, 2019 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, such as in the the Principal Component Analysis method or PCA. In this tutorial, you will discover the eigendecomposition, […]

Last Updated on August 14, 2020 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 get help with linear algebra for machine learning. After reading this post, you will know: Wikipedia articles and textbooks […]

Last Updated on August 9, 2019 All of the Linear Algebra Operations that You Need to Usein 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 find useful as a machine learning practitioner. This is a cheat sheet and all examples are short and assume you […]

Last Updated on October 18, 2019 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 in a wide array of applications including compressing, denoising, and data reduction. In this tutorial, you will discover the […]