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Euclidean Space Course

Euclidean Space Course
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.
Workload: between 4 and 360 hours

What our students are saying

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Really great course. Lots of valuable information.
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