University Linear Algebra
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.
Course Content
Unit 1 — Mathematical Foundations & Complex Numbers
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1.1 — Mathematical Preliminaries
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1.2 — The Axiomatic Method
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1.3 — Fields & Introducing Complex Numbers
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1.4 — Modulus, Argument & Polar Form
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1.5 — Complex Arithmetic & Conjugates
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1.6 — ℂ as a Field: Inequalities, Roots & Geometric Series