--- title: Matrix Algebra description: Matrix algebra focuses on the rules and operations governing matrix addition, multiplication, transposition, and inversion. You will understand how to manipulate matrix equations, calculate determinants, and apply these algebraic properties to solve systems of linear equations. category: mathematics subcategory: linear-algebra difficulty: beginner, intermediate, advanced url: /subject/matrix-algebra --- # Matrix Algebra Matrix algebra focuses on the rules and operations governing matrix addition, multiplication, transposition, and inversion. You will understand how to manipulate matrix equations, calculate determinants, and apply these algebraic properties to solve systems of linear equations. ## Available Resources 1 Videos • 2 Books • 6 Courses • 1 Websites ## Courses ### 1. Matrix Calculus for Machine Learning and Beyond (MIT 18.S096) **Author:** Alan Edelman, Steven G. Johnson Extends calculus to matrices and general vector spaces: derivatives as linear operators, Jacobians, derivatives of matrix factorizations, adjoint methods and automatic differentiation. 17 lecture videos, lecture notes, and problem sets with solutions teach learners to derive and compute gradients for large-scale optimization. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-s096-matrix-calculus-for-machine-learning-and-beyond-january-iap-2023/ **Tags:** matrix-calculus, automatic-differentiation, jacobians, adjoint-methods, gradient-based-optimization ### 2. Linear Algebra - Khan Academy Learn linear algebra fundamentals, including matrices, vectors, and transformations, with Khan Academy's comprehensive course. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/linear-algebra **Tags:** linear-algebra, matrices, vectors, linear-transformations, eigenvalues ### 3. Essence of Linear Algebra Grasp determinants with 3Blue1Brown's "Essence of Linear Algebra" course. Visualize and understand this key linear algebra concept. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab **Tags:** determinants, linear-algebra, linear-transformations, geometric-intuition ### 4. Linear Algebra (MIT 18.06) **Author:** Gilbert Strang Matrix theory and linear algebra: systems of equations, elimination, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and positive definite matrices. Includes 35 lecture videos plus problem sets and exams with solutions, giving the fluency needed for applied mathematics, engineering and data science. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/ **Tags:** linear-algebra, vector-spaces, eigenvalues, least-squares, matrix-factorization ### 5. Mathematics for Machine Learning: Linear Algebra In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you'll write code blocks and encounter Jupyter notebooks in Python, but don't worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning. **Difficulty:** Beginner | **Language:** English | **Duration:** 5 weeks of study, 2-5 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/linear-algebra-machine-learning **Tags:** courses, mathematics-statistics, linear-algebra ### 6. Matrix Algebra This course takes you through roughly three weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/linear-algebra/the-georgia-institute-of-technology-linear-algebra-ii-matrix-algebra **Tags:** courses, mathematics-statistics, linear-algebra ## Videos ### 1. Vectors | Chapter 1, Essence of Linear Algebra **Author:** Grant Sanderson Opening chapter of Grant Sanderson's animated linear algebra series, contrasting the physics, computer science and mathematics views of vectors. Shows vectors as arrows and coordinate lists, and how addition and scalar multiplication work geometrically, laying intuition for linear combinations and transformations. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=fNk_zzaMoSs **Tags:** linear-algebra, vectors, vector-addition, visual-intuition ## Books ### 1. Introduction to Linear Algebra, 6th Edition **Author:** Gilbert Strang The textbook behind MIT 18.06, now in its sixth edition. It builds elimination, augmented matrices, and LU factorization into the four-subspaces framework, so you can read off whether Ax=b has one solution, infinitely many, or none. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://math.mit.edu/~gs/linearalgebra/ila6/indexila6.html **Tags:** linear-algebra, gaussian-elimination, lu-factorization, four-subspaces, systems-of-equations ### 2. Matrix Analysis and Applied Linear Algebra **Author:** Carl D. Meyer Carl Meyer's SIAM textbook covering linear systems, vector spaces, norms and orthogonality, determinants, eigenvalues and Perron-Frobenius theory. Readers come away able to prove the core results and apply matrix factorizations to least squares, Markov chains and numerical problems. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0898714540?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, linear-algebra ## Websites ### 1. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/matrix-algebra