Matrix Decomposition: Using Eigendecomposition & Singular Value Decomposition

Math    |    Expert
  • 13 videos | 1h 24m 56s
  • Includes Assessment
  • Earns a Badge
Rating 4.7 of 3 users Rating 4.7 of 3 users (3)
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

  • 2m 24s
  • 4m 39s
  • Locked
    3.  Applying a Change of Basis Vectors
    5m 5s
  • Locked
    4.  Visualizing Eigenvectors and Eigenvalues
    8m 5s
  • Locked
    5.  Deriving the Characteristic Equation
    7m 21s
  • Locked
    6.  Computing Eigenvectors and Eigenvalues
    7m 33s
  • Locked
    7.  Exploring Properties of Eigenvalues and Eigenvectors
    7m 40s
  • Locked
    8.  Diagonalizing Matrices
    10m 21s
  • Locked
    9.  Eigendecomposition vs. Singular Value Decomposition
    6m 17s
  • Locked
    10.  Using Singular Value Decomposition with a Matrix
    7m 6s
  • Locked
    11.  Importing an Image for Singular Value Decomposition
    6m 2s
  • Locked
    12.  Performing Singular Value Decomposition on an Image
    10m 23s
  • Locked
    13.  Course Summary
    2m 1s

EARN A DIGITAL BADGE WHEN YOU COMPLETE THIS COURSE

Skillsoft is providing you the opportunity to earn a digital badge upon successful completion on some of our courses, which can be shared on any social network or business platform.

Digital badges are yours to keep, forever.

YOU MIGHT ALSO LIKE

Book Differential Equations with Mathematica, Fifth Edition
Book Numerical Methods Using Kotlin: For Data Science, Analysis, and Engineering
Book Advanced Data Structures and Algorithms: Learn How to Enhance Data Processing with More Complex and Advanced Data Structures

PEOPLE WHO VIEWED THIS ALSO VIEWED THESE

Course Agile Foundations: Fundamentals
Rating 4.4 of 1482 users Rating 4.4 of 1482 users (1482)
Course Core Statistical Concepts: An Overview of Statistics & Sampling
Rating 4.5 of 57 users Rating 4.5 of 57 users (57)
Course SecOps Tool Landscape: Intro to Security Tools (SecTools)
Rating 4.9 of 13 users Rating 4.9 of 13 users (13)