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Euclidean Space Course

Euclidean Space Course
4 to 360h flexible workload
certificate valid in your country

What will I learn?

This course provides a clear pathway to mastering inner products, norms, angles, and distances in R^n, advancing to orthogonality, Gram-Schmidt process, and projections through practical numeric examples. Learners will describe subspaces, change coordinates, construct projection matrices, and utilize QR factorization for accurate computations in high dimensions.

Elevify advantages

Develop skills

  • Master subspaces in R^n by transitioning between span, basis, and linear equations efficiently.
  • Calculate inner products, norms, and angles in R^n with strong geometric understanding.
  • Construct and apply orthonormal bases using Gram-Schmidt and QR for robust proofs.
  • Implement orthogonal projections and least squares to address real-world R^n challenges.
  • Evaluate numerical stability, including conditioning, orthogonality preservation, 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.
Workload: between 4 and 360 hours

What our students say

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