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Last updated:

September 23, 2023


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


A First Course in Linear Algebra (UNSW). Taught by Professor N. J. Wildberger, this course presents a geometrical view of Linear Algebra, with a special orientation to applications and understanding of key concepts.

The subject naturally sits inside affine geometry, which is the natural setting for vectors. Flexibility in choosing coordinate frameworks is important for understanding the subject. Determinants also play a key role, and these are introduced in the context of multi-vectors in the sense of Grassmann. The course features a careful treatment of polynomial spaces, with applications to Stirling numbers and cubic splines.

Course Curriculum

  • Lecture 01 – Introduction to Linear Algebra Unlimited
  • Lecture 02 – Geometry with Vectors Unlimited
  • Lecture 03 – Center of Mass and Barycentric Coordinates Unlimited
  • Lecture 04 – Area and Volume Unlimited
  • Lecture 05 – Change of Coordinates and Determinants Unlimited
  • Lecture 06 – Applications of 2×2 Matrices Unlimited
  • Lecture 07 – More Applications of 2×2 Matrices Unlimited
  • Lecture 08 – Inverting 3×3 Matrices Unlimited
  • Lecture 09 – Three Dimensional Affine Geometry Unlimited
  • Lecture 10 – Equations in Lines and Planes in 3D Unlimited
  • Lecture 11 – Applications of 3×3 Matrices Unlimited
  • Lecture 12 – Generalized Dilations and Eigenvalues Unlimited
  • Lecture 13 – Solving a System of Linear Equations Unlimited
  • Lecture 14 – More Row Reduction with Parameters Unlimited
  • Lecture 15 – Applications of Row Reduction (Gaussian Elimination) I Unlimited
  • Lecture 16 – Applications of Row Reduction II Unlimited
  • Lecture 17 – Rank and Nullity of a Linear Transformation Unlimited
  • Lecture 18 – The Geometry of a System of Linear Equations Unlimited
  • Lecture 19 – Linear Algebra with Polynomials Unlimited
  • Lecture 20 – Bases of Polynomial Spaces Unlimited
  • Lecture 21 – More Bases of Polynomial Spaces Unlimited
  • Lecture 22 – Polynomials and Sequence Spaces Unlimited
  • Lecture 23 – Stirling Numbers and Pascal Triangles Unlimited
  • Lecture 24 – Cubic Splines (Bezier Curves) Using Linear Algebra Unlimited
  • Lecture 25 – Cubic Splines (Bezier Curves) Using Calculus Unlimited
  • Lecture 26 – Change of Basis and Taylor Coefficient Vectors Unlimited

About the instructor

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