Linear Mapping Course
This course provides a comprehensive guide to linear transformations, covering definitions, linearity tests, applications in R² and R³ including rotations, reflections, and projections. Students will gain expertise in kernels, images, rank-nullity theorem, matrix representations, and operators on polynomial spaces, while developing skills in clear notation and problem-solving for advanced math and modeling challenges.

4 to 360h flexible workload
certificate valid in your country
What will I learn?
Explore linear transformations through definitions, linearity verification, and practical applications in R² and R³ with rotations, reflections, projections. Master kernels, images, rank, nullity, matrix techniques, basis changes, and polynomial operators, emphasizing precise notation for reliable mathematical solutions.
Elevify advantages
Develop skills
- Master testing linearity in maps and identify affine transformations accurately.
- Construct matrices for rotations, reflections, and projections in R² and R³ efficiently.
- Calculate kernels, images, rank, and nullity, interpreting them geometrically.
- Apply matrices and basis changes to operators on R^n and polynomial spaces.
- Communicate linear algebra solutions with precise notation and proofs.
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 are saying
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