Algebra

Ax = 0 and proving a set of vectors is linearly independentPrefaceWelcome back to the fifth edition of my ongoing series on the basics of Linear Algebra, the foundational math behind machine learning. In my previous article, I walked through the matrix equation Ax = b. This essay will investigate the important concept of linear independence and how it connects to everything we’ve learned so far.This article would best serve readers if read in accompaniment with Linear Algebra and Its Applications by David C. Lay, Steven…

Why should the number of independent row vectors precisely equal the number of independent column vectors for all matrices?Continue reading on Towards Data Science » Why should the number of independent row vectors precisely equal the number of independent column vectors for all matrices?Continue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink to…

The humble matrix multiplication along with its inverse is almost exclusively what’s going on in many simple ML modelsContinue reading on Towards Data Science » The humble matrix multiplication along with its inverse is almost exclusively what’s going on in many simple ML modelsContinue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink…

But why should the columns of the first matrix match the rows of the second? Why not have the rows of both match?Continue reading on Towards Data Science » But why should the columns of the first matrix match the rows of the second? Why not have the rows of both match?Continue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink to the primary source is…

Seven of my Favourite Machine Learning BooksPhoto by Laura Kapfer on UnsplashIn my first ever blog post for Towards Data Science in 2019, I wrote about five of my favorite machine learning books — books that cover every aspect from basic linear algebra to modern deep learning.They were:Linear Algebra Done Right by Sheldon AxlerMathematical Statistics and Data Analysis by John A. RiceElements of Statistical Learning by Trevor Hastie et al.Neural Networks and Deep Learning by Michael NielsenDeep Learning by Ian Goodfellow…

Solving matrix equations Ax= bPrefaceWelcome back to the fourth edition of my ongoing series on the basics of Linear Algebra, the foundational math behind machine learning. In my previous article, I introduced vectors, linear combinations, and vector spans. This essay will take a look at the matrix equation Ax = b and we’ll see how the very principle of solving a system of linear equations is linked to the matrix equation.This article would best serve readers if read in accompaniment with Linear Algebra and Its…

Explore how to estimate regression parameter using R’s matrix operatorsPhoto by Breno Machado on UnsplashIntroductionI recently wrote an article that explored the matrix algebra and mathematical operations that sit behind linear regression. Now, while it’s certainly important to have a firm grasp of theoretical principles, nothing actually beats doing those calculations. So, in this follow up article, we’re going to look at how to implement those matrix operations using R.This article should be treated as a companion to…

Looking under the hood at the matrix operations behind linear regressionPhoto by Mingwei Lim on UnsplashIntroductionFor most, simple linear regression is a common starting point for understanding model-based estimation and model comparison. Regardless of whether you’re taking an introductory statistics or data science course, you can bet your bottom dollar that linear regression will crop up at some point. And there’s a good reason for it.Simple linear regression provides a natural extension of simple descriptive…

A gentle refresher on essential concepts and operations for data sciencePhoto by Viktor Forgacs on UnsplashIntroductionIn my previous post, I introduced some of the operations and concepts that are fundamental to linear algebra. This included vectors and matrices, as well as the transpose, dot product, and matrix multiplication operators. In this post, I’ll introduce some additional concepts that complement those discussed previously. If you haven’t already seen my primer on linear algebra you can check it out here.Linear…

Two high school students have proved the Pythagorean theorem in a way that one early 20th-century mathematician thought was impossible: using trigonometry. Calcea Johnson and Ne’Kiya Jackson, both at St. Mary’s Academy in New Orleans, announced their achievement last month at an American Mathematical Society meeting. “It’s an unparalleled feeling, honestly, because there’s just nothing like it, being able to do something that ... people don’t think that young people can do,” Johnson told WWL-TV, a New Orleans CBS…