Linear Algebra III: Determinants and Eigenvalues

Linear Algebra III: Determinants and Eigenvalues

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 determinants of using cofactor expansions and properties of determinants
  • Compute the area of regions in R^3 under a given linear transformation using determinants
  • Model and solve real-world problems using Markov chains
  • Verify that a given vector is an eigenvector of a matrix
  • Verify that a scalar is an eigenvalue of a matrix
  • Construct an eigenspace for a matrix
  • Characterize the invertibility of a matrix using determinants and eigenvalues
  • Apply theorems related to eigenvalues (for example, to characterize the invertibility of a matrix)
  • Factorize 2 × 2 matrices that have complex eigenvalues
  • Use eigenvalues to determine identify the rotation and dilation of a linear transform
  • Apply theorems to characterize matrices with complex eigenvalues
  • Apply matrix powers and theorems to characterize the long-term behavior of a Markov chain
  • Construct a transition matrix, a Markov Chain, and a Google Matrix for a given web, and compute the PageRank of the web.

Prerequisite

None.

Instructors

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

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