Euclidean Space Course
This course builds mastery of Euclidean space in R^n, covering subspaces, inner products, angles, orthogonality, Gram-Schmidt process, projections, and QR factorization. Students gain geometric intuition and computational skills vital for advanced math, data analysis, and numerical simulations in higher dimensions.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Explore Euclidean space in R^n through inner products, norms, angles, distances, orthogonality, Gram-Schmidt, and projections, supported by numeric examples. Learn to handle subspaces, coordinate changes, projection matrices, and QR factorization for accurate computations in multidimensional settings.
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.
- Construct 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 preservation.
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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