Euclidean Space Course
Dive into Euclidean spaces in R^n with this course, covering subspaces, inner products, angles, orthogonality, Gram-Schmidt, projections, and QR factorisation. Develop strong geometric understanding and computational techniques vital for advanced maths, data analytics, and numerical simulations, ensuring reliable problem-solving in complex scenarios.

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.What our students say
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