# Matrix Decomposition: Using Eigendecomposition & Singular Value Decomposition

Math    |    Expert
• 13 videos | 1h 24m 56s
• Includes Assessment
Eigenvalues, eigenvectors, and the Singular Value Decomposition (SVD) are the foundation of many important techniques, including the widely used method of Principal Components Analysis (PCA). Use this course to learn when and how to use these methods in your work. To start, investigate precisely what eigenvectors and eigenvalues are. Then, explore various examples of eigendecomposition in practice. Moving on, use eigenvalues and eigenvectors to diagonalize a matrix, noting why diagonalizing matrices is extremely efficient in computing matrix higher powers. By the end of the course, you'll be able to apply eigendecomposition and Singular Value Decomposition to diagonalize different types of matrices and efficiently compute higher powers of matrices in this manner.

## WHAT YOU WILL LEARN

• discover the key concepts covered in this course mathematically define eigenvectors and eigenvalues outline how to apply change of basis visualize eigenvalues and eigenvectors derive the characteristic equation compute eigenvalues and eigenvectors of a matrix explore properties of eigenvalues and eigenvectors
• diagonalize a matrix differentiate between eigendecomposition and Singular Value Decomposition (SVD) perform Singular Value Decomposition (SVD) on a matrix import an image to perform SVD simplify an image with SVD summarize the key concepts covered in this course

## IN THIS COURSE

• 1.
Course Overview
• 2.
The Purpose of Eigenvectors and Eigenvalues
• 3.
Applying a Change of Basis Vectors
• 4.
Visualizing Eigenvectors and Eigenvalues
• 5.
Deriving the Characteristic Equation
• 6.
Computing Eigenvectors and Eigenvalues
• 7.
Exploring Properties of Eigenvalues and Eigenvectors
• 8.
Diagonalizing Matrices
• 9.
Eigendecomposition vs. Singular Value Decomposition
• 10.
Using Singular Value Decomposition with a Matrix
• 11.
Importing an Image for Singular Value Decomposition
• 12.
Performing Singular Value Decomposition on an Image
• 13.
Course Summary

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