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Euclidean Space Course

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

What will I learn?

This course offers a clear pathway to grasp inner products, norms, angles, and distances in R^n, advancing to orthogonality, Gram-Schmidt process, and projections through practical numerical examples. Learners will master describing subspaces, coordinate transformations, projection matrices, and QR factorisation, acquiring essential skills for accurate computations in high-dimensional spaces.

Elevify advantages

Develop skills

  • Master subspaces in R^n by swiftly navigating span, basis, and linear equations.
  • Calculate inner products, norms, and angles in R^n using geometric perspectives.
  • Construct and apply orthonormal bases with Gram-Schmidt and QR for robust solutions.
  • Utilise orthogonal projections and least squares for real-world R^n challenges.
  • Evaluate numerical stability involving conditioning, orthogonality preservation, and reorthogonalisation.

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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Very great course. Lots of rich information.
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