Euclidean Space Course
Gain expertise in Euclidean space within R^n, covering subspaces, inner products, angles, orthogonality, Gram-Schmidt, projections, and QR factorisation. Develop geometric understanding and computational skills vital for advanced mathematics, data analysis, and numerical simulations in practical applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course provides a clear pathway to mastering inner products, norms, angles, and distances in R^n, advancing to orthogonality, Gram-Schmidt process, and projections through practical numeric examples. Learners will describe subspaces, change coordinates, construct projection matrices, and utilise 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 using geometric principles.
- Construct and apply orthonormal bases with Gram-Schmidt and QR for robust solutions.
- Implement orthogonal projections and least squares for 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.What our students say
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