This is an one year course of basic idea and technique of Linear Algebra. The materials for the first semester are as follow:

1. Review and basic setting of vectors, inner product and matrices.
2. Solving linear equations (in the case of square matrices), Gauss elimination algorithm, inverse matrices, basic factorization of square matrices
3. Solving linear equations (general case); vector spaces and subspaces; null space and rank; fundamental theorem of linear algebra; basis and dimension.
4. The notion of orthogonality; projections; Gram-Schmidt.
5. Determinant; Cramer’s Rule; Volume.