- 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

The first introductory lecture in linear algebra for General Mathematics, Financial Mathematics, and Information

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Basic matrix operations, systems of linear equations, arithmetic vector spaces, linear dependence, linear envelope, dimension, orthogonality and orthogonalization, matrix decompositions, least squares problem, determinants.