Linear Algebra II: Matrix Algebra

Linear Algebra II: Matrix Algebra

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:

  • Apply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.
  • Apply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.
  • Characterize the invertibility of a matrix using the Invertible Matrix Theorem.
  • Apply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.
  • Compute an LU factorization of a matrix and apply the LU factorization to solve systems of equations.
  • Apply matrix algebra and inverses to solve and analyze Leontif Input-Output problems.
  • Construct transformation matrices to represent composite transforms in 2D and 3D using homogeneous coordinates.
  • Construct a basis for a subspace.
  • Calculate the coordinates of a vector in a given basis.
  • Characterize a matrix using the concepts of rank, column space, and null space.
  • Apply the Rank, Basis, and Matrix Invertibility theorems to describe matrices, subspaces, and systems.

Prerequisite

None.

Instructors

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

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