--- title: Determinants description: Determinants are scalar values computed from square matrices that characterize their invertibility and scaling properties. Learners will understand how to calculate determinants, use Cramer's rule, and analyze volume changes under linear transformations. category: mathematics subcategory: linear-algebra difficulty: beginner, intermediate, advanced url: /subject/determinants --- # Determinants Determinants are scalar values computed from square matrices that characterize their invertibility and scaling properties. Learners will understand how to calculate determinants, use Cramer's rule, and analyze volume changes under linear transformations. ## Where to start Start with 3Blue1Brown's Essence of Linear Algebra, a free, visual beginner course that builds intuition for what a determinant means. If you only use one resource, make it Gilbert Strang's Linear Algebra (MIT 18.06) on MIT OpenCourseWare, a free course with 35 lecture videos, problem sets and exams with solutions. For a textbook treatment, continue with Linear Algebra by Stephen H. Friedberg and Arnold J. Insel. ## Available Resources 1 Books • 3 Courses • 1 Websites ## Courses ### 1. 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 ### 2. 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 ### 3. 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 ## Books ### 1. Linear Algebra Linear Algebra - A book resource **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0534422004?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/determinants