Matrix Decomposition: Using Eigendecomposition & Singular Value Decomposition

Math    |    Expert
  • 13 Videos | 1h 24m 56s
  • Includes Assessment
  • Earns a Badge
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

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

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