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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 path to grasp inner products, norms, angles, and distances in R^n, advancing to orthogonality, Gram-Schmidt process, and projections using straightforward numerical examples. Learners will describe subspaces, change coordinates, construct projection matrices, and utilise QR factorisation for accurate computations in higher dimensions.

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 with strong geometric understanding.
  • Construct and apply orthonormal bases using Gram-Schmidt and QR for robust solutions.
  • Use orthogonal projections and least squares to tackle real-world R^n challenges.
  • Evaluate numerical stability, including 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 valuable information.
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