Euclidean Space Course
Dive into Euclidean space in R^n, covering subspaces, inner products, angles, orthogonality, Gram-Schmidt, projections, and QR factorisation. Develop geometric understanding and computational skills vital for advanced maths, data analysis, and numerical modelling in New Zealand contexts.

4 to 360 hours 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 use QR factorisation for accurate computations in high dimensions.
Elevify advantages
Develop skills
- Master subspaces in R^n by switching between 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 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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