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.
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September 23, 2023
English
English [CC]
Description
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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