Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

Course
en
English
15 h
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Source
  • From www.edx.org
Conditions
  • Self-paced
  • Free Access
  • Fee-based Certificate
More info
  • 3 Sequences
  • Intermediate Level

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Course details

Syllabus

Upon completion of this course, learners will be able to:

  • Compute dot product of two vectors, length of a vector, distance between points, and angles between vectors
  • Apply theorems related to orthogonal complements, and their relationships to Row and Null
    space, to characterize vectors and linear systems
  • Compute orthogonal projections and distances to express a vector as a linear combination of orthogonal vectors, construct vector approximations using projections, and characterize bases for subspaces, and construct orthonormal bases
  • Apply the iterative Gram Schmidt Process, and the QR decomposition, to construct an orthogonal basis
  • Construct the QR factorization of a matrix
  • Characterize properties of a matrix using its QR decomposition
  • Compute general solutions and least squares errors to least squares problems using the normal
    equations and the QR decomposition
  • Apply least-squares and multiple regression to construct a linear model from a set of data
    points
  • Apply least-squares to fit polynomials and other curves to data
  • Construct an orthogonal diagonalization of a symmetric matrix
  • Construct a spectral decomposition of a matrix

Prerequisite

None.

Instructors

Greg Mayer
Academic Professional in the School of Mathematics
Georgia Tech (Georgia Institute of Technology)

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