Euclidean Space Course
Explore Euclidean space in R^n, covering subspaces, inner products, angles, orthogonality, Gram-Schmidt, projections, and QR factorisation. Develop geometric intuition and computational skills vital for advanced mathematics, data analysis, and numerical modelling, ensuring proficiency in handling multidimensional problems with precision and reliability.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This course provides a structured journey to master inner products, norms, angles, and distances in R^n, advancing to orthogonality, Gram-Schmidt process, and projections through clear numerical examples. Learners will describe subspaces, change coordinates, construct projection matrices, and utilise QR factorisation for accurate computations in higher 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 understanding.
- Construct and apply orthonormal bases using Gram-Schmidt and QR for robust proofs.
- Employ orthogonal projections and least squares to address 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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