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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 provides a clear route to mastering inner products, norms, angles, and distances in R^n, advancing to orthogonality, Gram-Schmidt process, and projections through practical numerical examples. Learners will describe subspaces, change coordinates, construct projection matrices, and use QR factorisation for accurate computations in high 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 insight.
  • 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

Your lessons are perfect. I purchased the one-year package and finally have the opportunity to follow various topics of my interest without needing to change platforms... I thank you for everything you do, I've already recommended you to other people...
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Giulio CarloDigital Marketing Student
I like how the lessons are straight to the point and how I can change chapters and skip content I don't need.
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Mariana FerresPhotography Student
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The platform is fast, simple to use. The diversity of content and complementary videos help a lot with learning.
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