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Diagonalization Course

Diagonalization Course
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.
Workload: between 4 and 360 hours

What our students say

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