The student will acquire the basic concepts of:
1. Complex numbers.
2. Linear systems.
3. Matrix and vector algebra.
4. The determinant of a square matrix.
5. Vector subspaces in Rn and other vector spaces.
6. Eigenvalues and eigenvectors of square matrices.
7. Orthogonality and orthonormality of vectors in Rn.

The student will acquire the skills that enable them:
1. To work with complex numbers.
2. To decide about the existence and uniqueness of solutions for a system of linear equations.
3. To find, in the case when they exist, the solutions of a system of linear equations.
4. To work with vectors and matrices.
5. To compute, in the case when it exists, the inverse of a square matrix.
6. To find bases for a vector space or subspace.
7. To compute the eigenvalues and eigenvectors of a square matrix.
8. To decide whether a square matrix is diagonalizable or not.
9. To obtain an orthonormal basis from an arbitrary basis.
10. To solve least-squares problems.
11. To orthogonally diagonalize a symmetric matrix.