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