Euclidean Space Course
This course teaches Euclidean space in R^n, focusing on subspaces, inner products, angles, orthogonality, Gram-Schmidt, projections, and QR factorization. It builds geometric understanding and computational skills vital for advanced math, data analysis, and numerical modeling in higher dimensions.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course provides a clear path to mastering inner products, norms, angles, and distances in R^n. It covers orthogonality, Gram-Schmidt process, and projections with practical numeric examples. Learners will describe subspaces, change coordinates, construct projection matrices, and use QR factorization for reliable high-dimensional computations.
Elevify advantages
Develop skills
- Master subspaces in R^n by switching between span, basis, and linear equations.
- Compute inner products, norms, and angles in R^n using geometric insights.
- Build and apply orthonormal bases with Gram-Schmidt and QR methods.
- Use orthogonal projections and least squares for R^n problem-solving.
- Evaluate numerical stability including conditioning and orthogonality.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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