This course is an introduction to linear algebra. Topics we will cover include basic properties of systems of linear equations, matrices and matrix algebra, determinants, vector spaces, subspaces, linear independence of vectors, basis and dimension of subspaces, linear transformations, eigenvalues and eigenvectors of a matrix, orthogonality of vectors, inner product and length of vectors.
Coordinate vectors, Coordinate Mapping for general vector spaces. Part I
Linear (in)dependence and Bases for general vector spaces
Kernel and Range of linear transformations
Examples of vector spaces in Computer Science
Abstract definition of vector spaces, subspaces, linear (in)dependence and examples
Cramer’s Rule, formula for inverse of a matrix and the geometric description of determinants
Some properties of determinants that can useful for computations
Introduction to Determinants
Dimension of spaces and Rank of a matrix
Review II for Midterm I exam
Review I for Midterm I exam
Subspaces of R^n
Inverse of a Matrix
Sum and multiplication of matrices
The standard Matrix of a Linear Transformation
Introduction to Linear Transformations
Introduction to linear (in)dependence
Describing solution sets in the parametric vector form
A new way to see linear systems: matrices acting on vectors.
Introduction to vectors
Describing solutions of a Linear System in the parametric way.
The Algorithm to obtain the reduced echelon form of a matrix. Useful to solve linear systems.
Proof that if a linear system has two distinct solutions, then it has infinitely many solutions.
Echelon Forms of Matrices
Encoding a linear system into a matrix
Defining the basic rules to solve linear systems
Presentation covering the basic definitions of the course.