Advanced Linear Algebra

An Interactive Journey

A rigorous, visualization-driven course through graduate-level linear algebra, following Steven Roman's celebrated text (Springer GTM 135, 3rd Edition).

Course Roadmap

Part I: Basic Linear Algebra

  • Ch 0: Preliminaries
  • Ch 1: Vector Spaces
  • Ch 2: Linear Transformations
  • Ch 3: The Isomorphism Theorems
  • Ch 4: Modules I: Basic Properties
  • Ch 5: Modules II: Free & Noetherian
  • Ch 6: Modules over a PID
  • Ch 7: Structure of a Linear Operator
  • Ch 8: Eigenvalues & Eigenvectors
  • Ch 9: Inner Product Spaces
  • Ch 10: Normal Operators

Part II: Topics

  • Ch 11: Bilinear Forms
  • Ch 12: Metric Spaces
  • Ch 13: Hilbert Spaces
  • Ch 14: Tensor Products
  • Ch 15: Positive Solutions / Convexity
  • Ch 16: Affine Geometry
  • Ch 17: SVD & Moore-Penrose
  • Ch 18: Algebras
  • Ch 19: The Umbral Calculus

Select a chapter from the sidebar to begin.