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Euclidean Space Course

Euclidean Space Course
from 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. It progresses 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 proofs.
  • Use orthogonal projections and least squares to tackle real-world R^n challenges.
  • Evaluate numerical stability including conditioning, orthogonality loss, and reorthogonalisation.

Suggested summary

Before starting, you can change the chapters and 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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