Diagonalization Course
Master diagonalisation from the ground up, covering eigenvalues, eigenvectors, Jordan normal form, and singular value decomposition. This course builds rigorous theoretical understanding alongside practical computational skills. Whether your goal is solving differential equations, analysing networks, or applying PCA, every concept connects directly to real applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course takes you through the complete theory and practice of matrix diagonalisation. You will learn to compute eigenvalues and eigenvectors, determine when a matrix is diagonalisable, and construct the factorisation A = PDP⁻¹ step by step. You will extend these skills to symmetric matrices, Jordan normal form, and singular value decomposition. Applications include solving linear ODEs, performing principal component analysis, and analysing graph spectra. Numerical methods and stability considerations are also covered so you can work confidently with large-scale problems.
Elevify advantages
Develop skills
- Eigenvalue Computation: Calculate eigenvalues and eigenvectors for any square matrix accurately.
- Diagonalisation Factorisation: Construct the full A = PDP⁻¹ decomposition from scratch.
- Spectral Theorem Application: Orthogonally diagonalise real symmetric matrices using the spectral theorem.
- SVD Analysis: Decompose rectangular matrices using singular value decomposition for real-world data problems.
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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