Syllabus
- fields, characteristic of a field,
- systems of linear equations, Gauss elimination, parametric form of the solution set
- elements of matrix operations, matrix as a linear mapping, group of regular matrices
- abstract vector spaces, linear independence, linear span, basis, dimension, rank of a matrix, fundamental subspaces of a matrix,
- linear mapping, matrix of a linear mapping, change of basis, space of linear mappings,
- determinant, geometric meaning, Vandermond matrix
Annotation
The first introductory lecture in linear algebra for General Mathematics, Financial Mathematics, and Information
Security.
Basic matrix operations, systems of linear equations, arithmetic vector spaces, linear dependence, linear envelope, dimension, orthogonality and orthogonalization, matrix decompositions, least squares problem, determinants.