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HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 3: Orthonormal Columns in Q Give Q’Q = I
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018

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Lecture 3: Orthonormal Columns in Q Give Q’Q = I

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Lecture 4: Eigenvalues and Eigenvectors

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Description

This lecture focuses on orthogonal matrices and subspaces. Professor Strang reviews the four fundamental subspaces: column space C(A), row space C(AT), nullspace N(A), left nullspace N(AT).

Summary

Examples:

  • Rotations
  • Reflections
  • Hadamard matrices
  • Haar wavelets
  • Discrete Fourier Transform (DFT)
  • Complex inner product

Related section in textbook: I.5

Instructor: Prof. Gilbert Strang