# InfoCoBuild

## A First Course in Linear Algebra

A First Course in Linear Algebra (UNSW). Taught by Professor N. J. Wildberger, this course presents a geometrical view to Linear Algebra, with 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.

 Introduction

 Lecture 01 - Introduction to Linear Algebra Lecture 02 - Geometry with Vectors Lecture 03 - Center of Mass and Barycentric Coordinates Lecture 04 - Area and Volume Lecture 05 - Change of Coordinates and Determinants Lecture 06 - Applications of 2x2 Matrices Lecture 07 - More Applications of 2x2 Matrices Lecture 08 - Inverting 3x3 Matrices Lecture 09 - Three Dimensional Affine Geometry Lecture 10 - Equations in Lines and Planes in 3D Lecture 11 - Applications of 3x3 Matrices Lecture 12 - Generalized Dilations and Eigenvalues Lecture 13 - Solving a System of Linear Equations Lecture 14 - More Row Reduction with Parameters Lecture 15 - Applications of Row Reduction (Gaussian Elimination) I Lecture 16 - Applications of Row Reduction II Lecture 17 - Rank and Nullity of a Linear Transformation Lecture 18 - The Geometry of a System of Linear Equations Lecture 19 - Linear Algebra with Polynomials Lecture 20 - Bases of Polynomial Spaces Lecture 21 - More Bases of Polynomial Spaces Lecture 22 - Polynomials and Sequence Spaces Lecture 23 - Stirling Numbers and Pascal Triangles Lecture 24 - Cubic Splines (Bezier Curves) Using Linear Algebra Lecture 25 - Cubic Splines (Bezier Curves) Using Calculus Lecture 26 - Change of Basis and Taylor Coefficient Vectors