**MATH 260. Basic Linear Algebra: (Last update: 08.03.2017) **

**Textbook:** Cemal Koç. Basic Linear Algebra. 2009

**Lecture 1:** Matrices.

**Lectures 2-3:** Row Equivalence. Invertibility. Elementary Matrices.

**Lecture 4:** Systems of Linear Equations. Homogeneous Systems.

**Lectures 5-6:** Determinants. Properties of Determinants.

**Problem section I:** Matrices.
Systems of Linear Equations. Determinants.

**Lecture 7:** Vector Spaces.

**Lecture 8:** Linear Independence. Linear Dependence. Bases. Dimension.

**Lecture 9:** Summary of Basis and Dimension.

**Lecture 10:** Inner Products. Orthogonality.

**Lecture 11:** Orthogonal and Orthonormal Bases. Orthogonal projections.

**Problem section II:** Vector spaces.
Inner product spaces.

**Lecture 12:** Diagonalization.

**Lecture 13:** Diagonalization of Real Symmetric Matrices.

**Lecture 14:** Linear Transformations.

**Lecture 15 (Optional):** Quadratic forms.

**Problem section III:**
Diagonalization. Linear Transformations.