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Linear Algebra II

790

A theoretical course on the fundamental concepts and theorems of linear algebra. Topics covered are: vector space, basis, dimension, subspace, norm, inner product, Banach space, Hilbert space, orthonormal basis, positive definite matrix, minimal polynomial, diagonalization and other canonical forms, Cayley-Hamilton, spectral radius, dual space, quotient space.

Text: 

Advanced Linear Algebra, Cooperstein, 2nd edition, CRC Press.

Prerequisite: 
Credit Hours: 
3

Topics to be covered:

  1. Vector Spaces
  2. Linear Transformations
  3. Polynomials
  4. Theory of a Single Linear Operator
  5. Normed and Inner Product Spaces
  6. Linear Operators on Inner Product Spaces
  7. Trace and Determinant of a Linear Operator
  8. Bilinear Forms
  9. Sesquilinear Forms and Unitary Geometry
  10. Tensor Products
  11. Linear Groups and Groups of Isometries
  12. Additional Topics in Linear Algebra
  13. Applications of Linear Algebra

(Dao 2017 )

Frequency: 
Every Fall Semester

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