University Linear Algebra

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About Course

University Linear Algebra builds the subject from first principles — fields and complex numbers, vector spaces and subspaces, norms and inner products, linear systems, linear maps and operators, determinants, matrix decompositions, the adjoint, and eigenvalues. It follows the rigorous, proof-aware approach used in first-year engineering linear algebra at the University of Waterloo (NE 112), the standard most Ontario students meet in their first university term. Every lesson pairs clear definitions and fully worked examples with graded A–D practice and a success-criteria self-check, so you always know exactly what you can do and where you need support. Concepts are illustrated with interactive graphs, and the computational methods connect to MATLAB/Python where it matters. When your results fall short on a topic, one-on-one iAscend tutoring is one click away.

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Course Content

Unit 1 — Mathematical Foundations & Complex Numbers

  • 1.1 — Mathematical Preliminaries
  • 1.2 — The Axiomatic Method
  • 1.3 — Fields & Introducing Complex Numbers
  • 1.4 — Modulus, Argument & Polar Form
  • 1.5 — Complex Arithmetic & Conjugates
  • 1.6 — ℂ as a Field: Inequalities, Roots & Geometric Series

Unit 2 — Vectors and Vector Spaces

Unit 3 — Subspaces

Unit 4 — Normed Vector Spaces

Unit 5 — Inner Product Spaces

Unit 6 — Linear Systems, Independence & Bases

Unit 7 — Real 3-Dimensional Space

Unit 8 — Linear Maps & Operators

Unit 9 — Linear Operators on Finite-Dimensional Spaces

Unit 10 — Matrix Decompositions

Unit 11 — The Adjoint of Linear Maps

Unit 12 — Eigenvalues & Eigenvectors

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