Euclidean Space Course
Dive deep into Euclidean space in R^n, covering subspaces, inner products, angles, orthogonality, Gram-Schmidt, projections, and QR factorization. Gain solid geometric understanding and practical computational skills vital for advanced math, data analysis, and numerical modeling in real-world scenarios.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course guides you to grasp inner products, norms, angles, and distances in R^n, then swiftly tackle orthogonality, Gram-Schmidt process, and projections using straightforward numeric examples. You'll describe subspaces, change coordinates, construct projection matrices, and use QR factorization, picking up hands-on tools for accurate calculations in higher dimensions.
Elevify advantages
Develop skills
- Master subspaces in R^n: switch between span, basis, and linear equations swiftly.
- Calculate inner products, norms, and angles in R^n with strong geometric insight.
- Construct and apply orthonormal bases using Gram-Schmidt and QR for solid proofs.
- Use orthogonal projections and least squares to tackle real R^n challenges.
- Evaluate numerical stability: conditioning, orthogonality loss, and reorthogonalization.
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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